I would like to add my 2 cents considering i have been looking for an unarmed build that can go up front and beat stuff up on a regular basis for quite some time, the Brawler seems to fit that need quite nicely on first glance.
D10 HD, full BAB and ability to overcome DR is a nice start. Especially the DR part reduces the need for an AoMF and still lets you deal damage on higher levels.
But on second glance the main prolem in comparison to normal TWF builds remains(and please this is not meant as a discussion about TWF, i think there has been enough of that, but i think this should at least be the benchmark here):
The flexibility, choice of materials and variety of critical hit ranges and multipliers is just not there. Plus to get any bonus to attack/damage, you once again need the AoMF which in return lowers your AC even more, even though you do not even have access to medium or heavy armor. Not to speak of enchantments.
Now the thing with TWF is that in order to deal significant damage you need to full attack considering Power Attack is just not an option. And you need a good attack bonus, because the penalty for TWF makes hitting that much harder, especially on the later iteratives. So in the best case you can move fast and especially have a high ini, so you at least get one or two full attacks in.
And i think here lies the most frustrating part of the Brawler. You do not get Masterwork transformation, you do not get weapon training, you cannot as cheaply enchant your unarmed strikes (AoMF) and also give up a slot doing so and you can not add any other enchantment. Of course the argument here is, well you get more damage dice but if you cannot hit whoever is in front of you it does not do you any good whatsoever. Especially considering that we are talking about a bonus damage of maybe 1 up until 12th level. Just to throw it out there, by that level with the two weapon warrior archetype you can be dual-wielding Falcatas like light weapons with 19-20/*3 crit!!!
Which brings me to the crit point. Not only are we talking obvious damage, we are also talking a whole row of feats which would be perfectly suited for use with Martial Maneuvers. But that would only fly if at least the crit range went up.
Now your solution to just let the Brawler use more weapons really goes against what i think should be the point of this class: A guy who pummels you with his fists/body.
More weapons just is like saying: We know unarmed strike sucks, we do not know how to fix it so here is some weapons so you can build a two weapon fighter just that he cannot use proper armor and is lacking in feats. If you have to, let cestus or brass knuckles be part of the flurry, but i think that is just a cheap fix, not a proper solution
Yes you do not need the Dex like you would for a two weapon fighter. But you also loose a lot of Armor and especially feats (like two weapon rend for instance).
And please, you have to change the required time for martial maneuvers to a swift action. As i just said, in order to deal damage two weapon fighting (or brawlers flurry) you need to full attack, which means you spend your first turn moving towards your enemy (for instance with a charge) to try and clobber him the next. If you can't move because you want to power up with martial maneuvers, well you might start dealing damage in round 3. And by that time your one move action might not be enough, so you might just end up full attacking in round 4...
Now i do have an idea how to fix this, and it might just fix unarmed strike for the brawler:
If the brawler has his body forged into a weapon, why not have some weird wizards/crazy alchemists that like to tinker wíth humans enchant his unarmed strike. Because you need to find such a special character, the cost is 100% more than with a normal weapon.
That way you are not unfair when it comes to pricing compared to fighting with two weapons, you still do not have the masterwork transformation or material choices (especially at lower levels) and you can still use your neck slot to boost your already low armor. It would fix the criticism most heard when it comes to amulet of mighty fists and offer the same benefit, at the same price just without the drawbacks.
You still take a lot of hits, but this would fit the brawler theme, where you have a guy who does not use weapons, why would he wear heavy armor? And you don't have to use the workaround of allowing weapons.
If you then put the crit range at 19-20, it might seem overpowered, but you have no class features enhancing your attack regularly, so the chance for your iteratives to hit is significantly lower.
This way the Brawler would do enough damage to compete, not do too much and really offer a different style of character, one that focuses on unarmed strikes and some martial maneuvers. If you leave the option for body enchantment as a class feature, it will really be unique and go into more being a class of his own.
Now i hope someone takes the time to read this, for all the others:
TL;DR
The shortcomings of unarmed strike compared to weapons could be fixed by allowing the Brawler to have his unarmed strike enchanted at twice the normal cost. If you add an expanded crit range and maybe martial maneuvers as a swift action, you end up with an unarmed build that can compete damage wise while offering unique flavor.