I don't have a BAR, I have Garands. As a general rule, faster burning powders are better than slower burning in gas guns.This all has to do with the residual breech pressure at unlock. These guns were designed to unlock while there still is some pressure in the barrel, this pressure helps pop the case out of the chamber. The pressure is on the order of 650 psia. If you are using a powder that gives too high of a breech pressure, you will rip rims, and you will over accelerate the mechanism, leading to battering and malfunctions.
For 30-06 Garands, for decades the advice has been not to use powders faster than IMR 3031 and not slower than IMR 4064. IMR 4895 was the service rifle powder, it was used as the 30-06 propellant in WW2, Korea, etc. It was the powder used in the National Match ammunition. For 30-06 semi auto, any of the 4895 powders, that is H4895, AA2495, or IMR 4895, should be the first choice for experimentation.
I would not use 190 grain bullets, I would stay with bullets from 150 grains to 175 grains, though shooting lighter bullets than 150 grains is just fine. Heavier bullets cause function issues, mainly gas port pressure issue.
I doubt Browning will provide any advice about reloading, but you could call them and ask if the mechanism will handle 190 gr factory ammunition.