You're really gonna have to decide if you want a viable big game caliber or not.
I would not have a problem using a 6.5 to 7mm for big game. YMMV.
For me, 180 grains at 3000 fps is about all the recoil I want to manage for a LR shot. The 7's deliver that in spades. If you're gonna run a brake, that's another thing.
So there's no easy answer here!