Building around Brawn is a bit harder than using Moxxi, granted, but its far from impossible.
You just need to tailor your gear around it.
First off…why the FotF ?
I understand its purpose in a Moxxi build where it keeps your health full by dealing damage around you, but in a brawn build, having a shield that is useful only when depleted is a bit counterproductive. I would take advantage of having all your health regen skills being % based and increase my base health (so that the same % of regen equals a bigger number of health)
My favorite shield for a Brawn setup is the Evo, with the Neo and RR as close second. (though the RR needs to be used with a different COM like a beast or monk for example)
For the same reason, your relic spot should be a blood of the ancient with around +50% extra health (and extra ammo of your choice)
Those 2 things together are enough to make the limited health regen from Brawn sufficient.
those 2 skills (along with the base damage bonus provided by the COM) are what allows you to concentrate on brawn and not lose DPS. I agree that a boost to Sexy-Trex would be a better choice, but those 2 are still great. One good way to stay alive is if everything shooting at you is dead 
Another thing of note: the flat damage bonus from the COM is about the only straight damage boost Sal can get, apart from I’m your huckleberry (which requires pistols and only works on one hand) and divergent likeness (which requires 2 of the same guns)
Don’t underestimate a small damage bonus like this when it’s then multiplied by 2 guns and by all those fire rate bonuses.
Not much wrong here, (though a single point in L&L would allow you to benefit from the COM bonus)
Don’t underestimate speed as an effective mean of damage mitigation: with 5/5 in Bus, you can effectively dodge bullets Neo. You can also reach cover easier, get better shot placement and outrun those suicide units. Bus is as much part of the Brawn survival toolbox as the other skills.
Here’s what I would use: http://bl2skills.com/gunzerker.html#550000501005045010514052215005051
I already commented on a few of those, let’s get to the rest.
With all the fire rate boosts you have available in a brawn build, it stands to reason that a semi-auto gun like the striker doesn’t take advantage of the build. I find the DPUH to be a poor choice for a Brawn build too because of its effective range: Usually, you can facetank anything with Sal, as your healing is dependent on the damage you deal, but in a brawn build, you healing is dependent on TIME instead, so you gain by being a bit farther away than what the Harold requires you to.
The lady fist is boring if you don’t have a second gun with high damage to take advantage of it, but its otherwise ok here I guess.
My personal recommendation would be dual Pimp or dual butcher: anything with a high DPS that still has reasonable accuracy at medium range. Dual Interfacer would probably be very good too 
