Factory TRD Off Road and TRD Pro wheels are 60mm offset. 35mm will give you a bit of poke, but with 12.5" wide tires, I agree you'll probably have to chop the cab mount.
For comparison sake, I have 35.1" Duratrac 285/75R18s. These are skinny 35s. I'm running a 2" lift up front from the factory TRD Pro suspension. I only had to remove the small mud guards in front of the front wheels. That's it. No cab mount chop. This setup works great for me.
With 12.5s, you may also rub a bit on the sway bar, but maybe not with that offset? A big plus to that offset will be the extra clearance it'll give you for aftermarket UCAs like you're planning on doing.
Guys also report rubbing on the front skid plate with wider tires. Depends on the plate and the offset, I guess.
That's a good size tire for the stock rims for sure, and clearance is easy for those.
I put 325/65r18 (35x13) Hankook ATMs with 18x9 +25 rims on mine and they actually have lower rolling resistance than the stock Bridgestones. Width actually tends to improve rolling resistance, though it will increase aero drag. The biggest variables are the compounds used and the construction. And... lifting the truck pretty much always increases aero drag.
I BMC'd mine but I probably could have avoided it by moving the wheels forward with the alignment cams. It would have been super tight though. I also moved the front plastic forward.
I didn't lift it at all (except for the tire radius increase), and it never bottoms out on the wheelwell. You don't *need* a lift for 35s on a Tundra; rather you need to to make fore-aft space if your tires stick out much more than stock. If you do a lift but don't increase fore-aft clearance, it'll still rub when suspension is compressed and you turn the wheels.