I would choose the 300 Mag between your two first choices in the OP. The 7MM is pretty close to the 270 in bullet weight range.
In my thinking the 300 gives you choices in good 150 grain loads to tame the recoil a bit. It offers 200+ weight range. The only real difference between the 7MM and 300 is the ability to use heavier bullets on moose and elk. The 300 Win Mag outperforms the 7MM at 175-180 grain bullets. Even if you don't hunt bear you might hunt in bear country and a heavy 308 sturdy bullet would add a comfort factor.
Full disclosure: I've owned a 7MM Rem Mag in a 700 and a 375 H&H Mag in a Ruger No.1 as my only magnum rifles. I never liked the 7MM and quickly sold it after a couple of seasons. It was a moose rifle and loaded with Partitions.
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