I'm aware of the 3 caliber deal. But don't count out the 260 Rem.
Its a pleasure to shoot and its flat trajectory is a plus. It beats out the swede by +/- 100fps with a milder recoil. My Sako in 260 Rem (rebarreled .308) is an amazing medium game stopper. I own 2 Sakos, one in 260 Rem, one in 7mmRM. I dig those Sakos.
If I were buying from your caliber selection, the 270 Win. would be the go-to in my opinion. Proven game stopper here in the US.
Recoil is tolerable, and can bag groundhogs to elk. I would say it bridges a few gaps.