270 Win..

90 grain hollow points for all things small up to yotes.
140 TSX for most things in N.A., including elk and mooseif get into that.

With the popularity of this caliber, it might be easier to find a left handed gun that you'dlike.

But since you already have a .22-250.. I'd still recommend the 270.. That way you can just hone one load (140 TSX) and just stay with that for all things bigger than dogs.