Get a 1:8 twist barrel for your rifle, and stay .22-250.
75Amaxs should make almost 3300 from a straight .250...
Blown the shoulder out, and you'll get near 3400 from a .22-250AI. That is a whole 'nutha animal from a slow twist .250 throwing light bullets...
A .22-243Win would be a step up from there. Simple neck down plentiful .243Win brass, and shoot.
A .22-243AI offers another step up in capacity. Mine throws a 75Amax @ 3600, easy peasy. If you run the ballistics on that combo, your eyebrows will lift! You pay the piper in barrel life, but who cares? (For the performance, I sure don't)
Stepping up to a larger bore, a .243AI throwing 105Amaxs @ ~3250 would be evil. But you're gonna have quite a bit more blast & recoil, and not as near as flat trajectory as the necked down version throwing a 75 ~400fps faster...
Unless you go with a monster of a 6.5mm, none offer the flat trajectory that I like for predator whacking. It allows for more of a 'fudge factor' for range estimation on the fly. And the muzzle blast just becomes too much, if you wanna watch your critter crumble in the scope and get on the next one, quickly...
Good luck & have fun!