If you liked the .280 but recoil was borderline a problem then simply get a 7mm-08. To 350 yards it gives up literally nothing to the .280 as factory loaded and it will take any non dangerous game on this continent reliably with out question.
It also was on the border of respect/fear as far as the recoil goes. See, soaking wet I'm maybe 145 on a good day. I'm a scrawny type dude, with little upper body strength. My .280 had just enough recoil that sometimes I could feel the scope barely touch the hairs on my eyebrow, but not enough to actually hit me.....
What I'm looking for is a rifle that can successfully hunt anything in North America, without having more recoil that my .280
30-06, .270 Weatherby, 300WSM, .270WSM, 7mm mag, 7mmWSM, etc...
ALL have more recoil than the .280 Remington.
Right now I'm thinking that a 30-06 with a muzzle brake and recoil pad would be my best suited choice,
FORGET about a muzzle brake. The excess noise they create will permanently damage your hearing with a single shot unless you are willing to wear some type of hearing protection in the woods with you when you hunt.