I've shot the Tikka T3 lite in 308, and it certainly had a fair bit of kick to it.
I'd be inclined to go for a 7mm 08 as it should do just as well as 308 but less recoil, I'm not recoil sensitive but I'd go for less recoil any day.
260rem would be another good calibre but ammo availability is nothing like the others you have mentioned.
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