For deer or black bear use, I don't think there is that much difference between a .243 or a .270, frankly, and I say this having shot over ten of each species with those calibres.
I firmly believe that bullets are way more important than bore size, but admittedly, talking about bullet design isn't as sexy as talking about calibers.
Both rifles are flat shooting, and if you REALLY want to trade in that .270, I'd step up to something with a lot more frontal area, like a .338/06 or .35 Whelen in standard calibers, or a .338 in a Magnum. Or even a .45/70 or .444 if you want something that's real fun to play with!
Recoil of most standard calibers vs. the .270 is inconsequential. The bigger magnums (say starting at the .300 Win) have more, but they're not that bad. The .338 on up are a bit testy on the bench, but in the field you will not notice it at all.
Best idea, I think, is to keep the .270 as a spare (just in case!) and just buy another gun. Lie to your wife that you won it in a store draw!
A guy just cannot have too many rifles!