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One would think the true fear & violence of the casting shouldn't happen until after the casting

Do not let him speak. When some strange wizard starts their incantation, that might be your final opportunity to strike them.

As the caster presumable would be aware of. Situations where player and character insight significantly differ are occasionally better resolved by informing the player of the forgotten mechanic, or in this case first secretly rolling diplomacy/society/perception if the character recognizes the consequence.
(One could also be nice to the player and consider whether an NPC could have Recognize Spell, and stand down their comrades on successful identification)

The time "paradox" still occurs frequently with fully aware players, though. It's tricky to make sense of in-world simultaneous events when regimented as sequential turns, especially in the transition from exploration to encounter - although easier when leaning into the heroic fantasy of things.

If a player's proclaimed action is the event that causes the transition, I run things in-between Mathmuse's fully free activity and RAW's potential for "triggering" combat at the end of the combat-round.

The inciter is offered a choice, with the benefit being a reaction to attempt their intention before their first turn. This reaction's trigger based on their initiative roll, at a significant bonus. However, their actual turn will start with a penalty to that roll.
(For two-action activities like this spell, they are also slowed 1 the first turn, and bigger actions have a bigger initiative-penalty.)

Simulation-wise, it feels far more appropriate than either extreme. I can somewhat make sense of a character being so slow on the draw that the world reacts before they pull the trigger. But struggle when someone rolling high on initiative gets off 5 actions before even their comrades have acted. In OPs case, where the caster rolled so low, they're sluggish enough that they have barely started the spell when the now enemies are at full assault.

Ludic-wise, it encourages creatively engaging with the world, while not being so impactfull players are disruptively incentivized , regretting any fireball they didn't throw while it was free. Players get a rewarding moment for leaning into whatever competency they've built their character for, but also need to offer some buy-in: If circumstances change too much, they risk delaying their turn for nothing (and wasting the spell).

If OPs player had rolled high, they might have been able to frantically explain before the first blow. Consequently, the failure to act quick enough would also be meaningful storytelling.

It's also a system it feels fair for the NPCs to benefit from, and supports some of my other inclinations in running encounters.

In terms of defence, the Archetype feats are costly compared to general feats into Armor Proficiency (although many other classes might want those class-feats more than the Wizard). While also requiring an action in combat to enter the stance and providing -1 effective AC until Mountain Stronghold. Mountain Stance is very much balanced around Monk's superiour unarmoured proficiency, so as a Wizard you don't benefit as much.

In terms of offence, Falling Stone only helps when you wouldn't want to to spend two actions on a spell (or other actions), and are in melee, and missed your first strike. That's highly conditional for the cost of a 6th lvl feat - especially as at level 6, you're already lagging behind in proficiency. At level 7, you could be master in Athletics, and Attack with that instead of strikes (with a Bola, you can even do this at range).

However, if you're not looking so much for the specific vibe of the kung-fu wizard, but a wizard-build where you enter a stance with defensive bonuses, and have actions to use for non-wizard thing, there's an alternative:

The Kineticist Archetype

At level 4, take Armor In Earth (or Hardwood Armor, or even Metal Carapace). At level 6+ take at least one Impulse-feat for actions to use when not spellcasting. Take the Armor Proficiency feat at the earliest opportunity.

Benefits:
* Relative +2 AC and Bulwark already at lvl 4 and for no extra feat cost, if Earth. If wood/metal, +1 and free shield-block on a free shield with some scaling.
* You can spend the action to activate the armor outside of combat. With Light Armor proficiency, you're also safer when its not up.
* Presumably some impulse would be desirable to spend actions on when not spellcasting. (Edit: Or not)
* The dedication feat is less demanding than Monk, and gives a bonus skill-proficiency compared to Martial Artist.
* (This general build also frees up your attributes to almost whatever you want. You need Int and +2 Con. You have a good reason to invest in strength, to avoid the movement and skill penalty - but as you're only taking the penalty when the impulse is active, you can avoid the penalty for the out-of-combat climb-check or in combats where you know you'll need mobility. While there's not much reason to not put that fourth attribute-boost to either strength or dexterity, the Kinetic-armored Wizard provides a rare opportunity to invest in Int and Cha without as substantial downsides.)
* Different vibes, if that's a benefit. Dwarf happens to have excellent attribute boosts and the perfect thematic fit for Armored in Earth, so I struggle to see the dwarven stone-attuned Wizard could not be appealing.

Downsides:
* Eats a general feat for light armour proficiency.
* Elemental Blast doesn't scale for free and isn't worth the cost - you won't be dealing damage from this.
* Less mobility when active if Earth and dumped strength.
* Different vibes, assuming that's a downside.
* There might not be any specific impulses you want. (Edit: In fact, this is quite likely. If you want the best armor-impulse for a Wizard, Earth's, you're stuck with other impulses that aren't the best for a Wizard. There's no other 1-4th level 1-action impulse that's generally useful in combat. Calcifying Sand provides a good reaction, but like the two-action combat impulses it suffers from your lower Archetype proficiency. Wood and Metal seems to both offer an aura with some defensive benefits as their best option. So you're still looking at Athletics to fill out the third action when spell-casting)

Could one spend those Archetype Feats on something else, and still have comparable benefits just from Armor Proficiency, Attribute investment and some other trick to spend your actions? Yes.
Is it mechanically better than Mountain Stance? Almost strictly better.
Is it better for you than Mountain Stance? That's up to you - I mostly posted this for future readers to consider if they stumble on this thread with a similar idea in mind, but if I've helped you that's great!

The counter-argument being that since you have rolled the die roll for the check and seen the result, that Fortune effect has already happened.

Refer to the section on Predetermined effect for the counter-counter. I suspect people's intuition would tend quite differently if for instance DaS was a coin-flip where you get a +1 or a -1 to the roll. You know the effect you're applying when applying Sure Strike. It's a distribution of outcomes tending towards higher values within the range. You know what effect you're applying when applying DaS. It's whatever you rolled when first making the roll.

In the case you're describing, one has already applied a fortune effect to alter the roll so the choice has been made. With DaS, you're not applying the effect until the strike action, you're just receiving information that benefits your decision making. No one is gonna send the Pinkertons after a DM who considers that too good to be true and rules differently than me. But it doesn't follow that the fortune effect has been applied to the roll just because one knows how the application will affect the roll.

Wait, what?

Wait, consider what I've written, then consider why I might have written it. Consider that I might in fact be aware of the distinction between fortune and misfortune and the relevant rules-text. What?

The argument, in a version often presented, is that you're not making the roll that Sure Strike gets to affect. If there's no such roll, no Ill Omen triggers either. Since it never applies, there never occures a conflict between Ill Omen and DaS - as only DaS goes through. I agree, it doesn't make sense, and Sure Strike's effect should be invoked at the same step that DaS' effect is.
(Note though - for no particular reason other than that it is cute - that if Ill Omen can negate a DaS-roll and Sure Strike can't, you could hypothetically end up in a niche situation where Ill Omen is a beneficial to an Investigator)

I certainly agree that there's a clear intuitive sense

If one reads the investigator and tries to understand how they work, imagining how it plays out on the table, it IMO seems weird to not have the intuition about DaS that makes it wonky with Sure Strike. It's only when trying to conceptualize an underlying structure for how Fortune-effects work and interacts that the challenge to this intuition presents itself. But I think the intuition should fall to that challenge.

At least in terms of raw hermeneutics, which is only a starting point for actual play. I also think that game-balance, this reading works just fine - but a DM being apprehensive about player's double-dipping into Fortune effects isn't Pinkerton-worthy. Sure Strike is somewhat cheaply accessible to an investigator. While the class isn't overpowered, one might want to avoid player's feeling they're playing the class wrong by not archetyping casters. Or just prevent a Magus with a free DaS from feeling overly awesome.
Eat Fortune, though, is a heavy investment for a minor cool interactions that isn't transparently excluded by RAW. While you're equally entitled as a DM to rule against it, it's the kind of dumbass build I'm absolutely here for and my heart sinks at the thought of a player being denied it.

Although in terms of consistent rulings based on RAW, it doesn't make sense to me to allow Eat Fortune and deny Sure Strike, though. (In the sense one would actually want to use either. One could decide that "use a fortune [...] effect" is when you make the action with the fortune trait, but in that case the trigger starts before the DaS-roll is determined.)

I can see several problems with that hypothetical ability. Not sure why it would have the Fortune trait, for one.

Presumably for similar reasons why Paizo have given Assurance the [fortune] trait in both its printings. It's a feat that alters how you determine the outcome of a roll. Which also happens to be how Paizo have chosen to define the nature of the (mis)Fortune trait.

The topic was touched on preMaster in this thread. As in this thread, the reasoning is largely caught up in the imagery of DaS, neglecting the (counter-)arguments for electability between DaS and Sure Strike.

"When you would roll to attack, instead of rolling the d20 randomly, place it down so it has the same number facing upwards as the DaS-roll."

Would one read the above phrasing as dominating Sure Strike? I think that's less likely. But while the imagery differs significantly, it implements the same mechanical framework. The presentation of DaS invokes the sense that it modifies the attack roll before the attacking action is made - but you're setting up an effect that will trigger later, as Sure Strike also does. The dice-maniupulation differs, but both can be conceptualized as taking place at the same step: After declaring the strike-action and a target, when you're about to roll you then apply the fortune effect to alter how that roll is made.

"A fortune effect beneficially alters how you roll your dice. You can never have more than one fortune effect alter a single roll. If multiple fortune effects would apply, you have to pick which to use."

When you're about to roll is the moment of application for both Sure Strike and DaS, and when you would have to choose between them. (As opposed to for instance Cat's Luck, which unambiguously applies at a later stage with a retroactive effect, and would be dominated by either DaS or Sure Strike)

Predetermined effect?
DaS' effect is previously determined, but the roll just generates a value that you later substitute in. Sure Strike is still stochastic after you've finished casting the spell - but that doesn't make it subdominant to other Fortune effects. If Slightly Lucky Stab [fortune] gave a +1 circumstance bonus to the roll, you could still choose between it and Sure Strike when rolling to stab. That would still be the case if Slightly Lucky Stab had you roll a d8 to pre-generate a -2 to +2 circumstance bonus. The substituting value being pre-generated hints at priority, but doesn't substantiate it.

Pre-roll?
In actual play, you're likely to roll the DaS-die, and then keep it around until the Strike is resolved. This creates a suggestive imagery that the DaS-die actually is the attack roll. But it's just a value that you substitute in. Conceptually, the step where the subsitution takes place is the same step you would apply Sure Strike's effect.

"Must"?
That DaS uses the word "must" is in the same sense Ill Omen uses "must" (see below). Ill Omen is undesirable to the striker, so stronger language is used to affirm that the effect is unavoidable. Sure Strike doesn't need that affirmation as you'll always want the effect, so space is saved by leaving it out - but mechanically it's equally unavoidable. "Must" doesn't do any actual mechanical work, it's just communicating underlying mechanics. DaS is sometimes undesirable, and shows up constantly when playing an Investigator, so it was deemed relevant to make the unavoidability explicit.

"Failure The first time during the duration that target rolls an attack roll or skill check, it must roll twice and take the worse result."

Unless one rules Ill Omen as superceeding Sure Strike, DaS' "must" doesn't interact with base assumptions of Fortune-effects.

Speaking of Ill Omen - if DaS superceeds Sure Strike, it also does Ill Omen, leaving Investigators practically immune to such Misfortunes. Which both seems kinda silly and kinda awesome. Nonetheless I think there is better justification for electability between Sure Strike and DaS than the latter dominating. There's plenty of ambiguity, though, and freedom for the DM to judge as befits their table - including forsaking possible RAW entirely for a preferred outcome as Graystone.

Homebrewing the core mechanics can be heavy-handed, even if it's the obvious option when players want the core mechanics changed. Introducing objects that enables the player fantasy has significant benefits.

Especially for something like this, where the rule have good reason for being what they are. After changing the rules, the table might come to better understand why the rules were as they were. But then changing them back is suddenly the cumbersome step. Items are far more plastic - if they're not outgrown or "lost", they might still change as all things in the world do. As players wield the Kris, it might grow stronger as they unlock its powers - or its powers slowly ebbs with use.

This touches on another benefit - items character encounter are part of the story being told. Introducing homebrew to the core mechanics adds additional steps before the players can step into the world. A well-crafted items helps bring the players into the world in addition to supporting the desired playstyle.

Items also have relation between cost and payoff for the players to consider, which gives them agency in how/whether they chose to leverage them. (Feats are similar objects in this respect, and well-crafted feats can also be great for drawing players into the fantasy of their character and the world.)

Although in this case, there already is a cost and payoff - dexterity-builds can easily be close to strength-builds in +strength damage on strikes. They just need to invest in strength as a secondary or tertiary ability. Presumably the don't want to do to make this investment because they want their character to be cool at what dexterity represents in the game while also being cool at a core aspect that Strength represents in the game while also being cool at what some other stat(s) represent in the game. But the game in question is one that forces players to prioritize what they want to be cool at. It's a core design-assumption that this is a good thing. You can't build a copy of the fantasy protagonist with high strength, dexterity and constitution, and also high wisdom, charisma and intelligence - because your posed with meaningful choices to make. While the power-fantasy might seem appealing, I wouldn't encourage taking those choices aways, as Dex-to-dmg does. While the suggested items can hopefully contribute to some creative consideration, they're not recommendations.

Feat-locking it is a good suggestion, assuming the players are finally wearing one down into foregoing well-crafted RAW. Another option worth considering is to introduce item effects. Below I'll explore some options for introducing dex-to-dmg, through specific magic weapons, runes, and consumable items. For instance, one could introduce a Specific Magic Weapon like this:

Kris of Player indulgence:
When rolling for damage from a strike with this +1 kris, replace the wielder's Dexterity modifier for the Strength modfier that is normally added.

Throwing this Kris into the game would a signficantly smaller commitment than homebrewingthe core game mechanics, and thus less disruptive. It's much harder for a strength-build (or mental stat-build) to begrudge the dexterious one unique item, but the complaining players would get what the request

Since you're dealing with several players, you could make this a unique set of weapons - three different kris[ses?] forged for some lore something something swords something people. Each kris has a unique effect - i.e. one adds the dex-mod as fire damage, one as cold and one as lightning or what have you. Every player will be able to hunt down a weapon for their character, but each weapon is markedly unique to the setting.

That it's a specific item means you get to lock the effect to less disruptive weapons. The kris has agile, finesse and deadly which are thematically appropriate. It also has a d4 damage-die, which partially offsets the +dex damage on a regular success compared to a d6 weapon - +4 dex +0 str deals as much damage with the Kris as +4 dex +3 str deals with a d6 weapon. Less than with a d8 weapon.
The interactions with item-rules is also beneficial. It effectively replaces property runes. That's a very payable cost until Flaming et al. becomes available.

Which happens to be an excellent point to survey which direction you want to take things. I'm somewhat sympathetic to 5e-players being upset with the lack of fin-Dex dmg when that's half their damage at low levels. But strength is an ever-diminishing proportion of damage dealt, while strength as a tertiary stat keeps catching up to Dexterity.

At higher levels, when characters are stacking potency runes, property runes and build features, it might be time to be a bit sterner about player expectations adjusting to the core framework of the game instead of the opposite. Giving them a specific magic item accomodates the players' request when they're least undeserving, without giving up much control on how it impacts the game. If you want players to have a bit more agency, though, you could introduce the:

Lesser Rune of Fatal Elegance - a level 3 weapon rune that can only be etched on finesse weapons:
Weapons empowered by this rune do not add the typical Strength attribute modifier to damage rolls. On a successful strike, the weapon deals additional precision damage equal to the average of your Strength and Dexterity modifiers.

This rune has a lot of similar benefits to the Kris. A rune is more exploitable in the sense that players can choose the runed weapon. This version of dex to dmg offsets that, however, by being a softer effect. A pure dex build, which would receive the most bonus damage, also deals the least damage with it - it's effectively the suggested half-dex to damage. You're still incentivized to invest into strength, but the pressure is lessened. There's less of a jump than with the Kris, where a player knowing they'll have access to it might completely neglect their strength and come to regret it once they outgrow the Kris.

Other property runes will eventually out-compete it when the time is ripe - but before level 8, runes are interesting but not as important to damage. If priced correctly, the rune would be a compelling option for dexterity-builds, but not so good one couldn't consider just investing in strength to have access to another rune.

A moderate rune that just adds dexterity to damage, and has some nice critical effect, should be fine to add around level 8. Assuming a +4 (soon +5) to damage, it's slightly ahead of the elemental runes' 1d6, which maintains the partially closed gap to strength builds' expected damage.

Potion of Dangerous Dexterity
Duration 1/10/60 minutes
While the potion is in effect, any succesfull melee strike adds your dexterity to damage. [Secondary effect that scales with potion level, maybe.] [Some downside, if you want to make it Dangerous Dexterity Mutagen, which prevents synergies with existing mutagens]

A consumable that lets you add dexterity to damage from finesse weapons. And non-finesse weapons. And lets the strength-build with decent dex benefit almost as much as you while the secondary-strength Dex-build is still ahead of you. Give them everything they've asked for and more, then see what happens.

Could also be a talisman that's attached to a melee weapon or handwraps, if you want to lessen the strain on action/hand-economy. A talisman activated for free would work well with a duration of 1 round, in addition to the above durations. That might be enough to indulge the fantasy, while obviously being less disruptive than doing the extra damage every round of the combat.