Many many good options list here. I feel like you already have a great if not ideal elk round.
I would gear my search for anything up to elk. IMO that means at the bottom end a 140 6.5 with a MV of 3k or very close. I know people have shot them with.243's and 25-06's long enough to fill a creek bottom but that's an extreme IMO.
I didn't catch any word of reloading or not. That plays a huge role in your choice.
If you don't reload, it's hard to beat the 7rm as a do all. If you want lighter in the recoil department you could go with a 7mm-08 (AI if you load), 280 Rem (AI / Sherman is on another level), 6.5x284 (limited ammo), 260 Rem (excellent AI round) or the 65 Creed at the bottom end.
Most of these are not the most commonly found on store shelves except for the creed (for now). If it's box ammo that's readily available then think about a 270 or 308.
You also didn't say if you were building or buying factory, that will play another huge role in choices.