While your concerns are near and dear to my heart Edge, I must respectfully disagree with your proposed solution. Clearly, we should be using SI naming schemes here to match PF2E's very timely switch to meters, centigrade, and kilograms in update v1.7. I suggest the following weapon names:
Greatsword -> Megasword
Longsword -> Kilosword
Shortsword -> Sword
Dagger -> Millisword
It'd be far more simple and elegant.
So where does the bastard sword fall in this system?
It doesn't. It is a BASTARD sword. It does not conform.
PF1e damage, with regard to crit, was consistent. Being able to set player expectations is important, and going in knowing that a crit would carve a real chunk out of someone was always nice. It wasn't jump-up-from-the-table-and-holler fun, but it certainly was worth a solid fist-pump.
PF2e damage, with regard to crit, is a lot of fun... when the dice are kind. You want to watch a player deflate? Let them roll that crit against the big bad and then get 1s and 2s on their bucket o' dice. Or I could reach into my way-back pocket and talk about my group's foray into Star Wars: Saga Edition, where our Soldier popped a Destiny point (auto-crit) for his Blaster Rifle (3d8) and managed 8 damage total.
One thing my group has done (for some d20-based games, we haven't tried it for PF2e yet) is that crits, rather than dealing double damage, become more cinematic. Lopping off limbs or setting the enemy prone and forced to run for 2 turns... things of that nature. Of course, crits work both ways, so watching the Paladin be stunned for a round and shaken for a round after that because the bugbear hit him really really hard has also made for rather interesting RP opportunities in combat.
But, separately from that, what bothers me is the critical success issue. Even with an Incredible task, I still have the same chance to critically succeed as the bumbling wizard to my left: a natural 20. The design goal with the 10+ rule for critical successes makes sense: if I'm really really good at something, I'm really only rolling to make sure I don't fail, rather than to make sure I succeed, so let my high rolls matter. This runs into the thematic issue outlined above, though, when the DCs are middling. Possibly the 'critical success' rules could be tweaked so allow a greater chance to critically succeed with higher training in the skill (beyond the 1...
I actually really like that last bit, the crit on 19 and 20 at legendary. Like Keen for skills. Most ideas I've seen push things to far as you alluded to but I really like that one, it's a nice and fun but reasonable effect.
Heck, I wouldn't even be opposed to toying with that idea further. Maybe at Master you crit on 19 and 20, and then at Legendary you crit 18, 19, or 20, and you don't auto crit-fail on a 1?
Hmm, the 18, 19, 20 is probably too much now I look at it but I like the idea of getting to ditch auto crit fails on a 1 (Though still crit failing if the 1 puts you at 10 or more below DC of course).
I agree that 18-20 is too much. I could see crit success on 19 at Expert, ignore crit-fail at Legendary.
Alternatively, ignoring crit-fail sounds more like a skill feat (and would be make more sense than the oddly juxtaposed Assurance feat we have today).