I think this is a great suggestion. The American I had shot great. Can’t remember if they differentiate action lengths which could limit your new cartridge selection.
I purchased my first last spring: TBAC Ultra 7. It’s on a 6.5 PRC with 19” barrel. I don’t bother with hearing protection while hunting, but I still do while practicing because “why not”. The recoil reduction is not as good as a brake alone, and the recoil impulse is more attenuated making it...
243, 6 Creed, 6.5 Creed, and 7mm-08 would be at the top of my list. If really limited to deer and close range shots, a 6.5 Grendel or 6 ARC also warrant consideration.
It’s hard to argue with a solid 30 caliber (’06, Win Mag, etc), but I like to shoot a lot to really develop confidence with my rifle. Recoil can be a factor in high volume work and a magnum 6.5 fits the bill nicely.