Utah,
I bought a limbsaver recoil pad for it and found it just fine for the Tikka in 300 WM. You are on the right track getting a long action caliber in the Tikka as even the short actions use the same overall action length so might as well get the long action advantage if you aren't gonna be saving the weight in getting a short action.
I got a .308 Win in Kimber Montana and have since moded it recently so it 4 pounds 12 oz for the rifle. All up with a scope its 5.5 pounds on the nose. I like the .308 for everything except coastal bears. Plenty for the moose, caribou, sheep, black bears, and even taken two grizz with a .308.
Bearguide is right the. The ballistics of the .284 (7mm) is tough to beat though. If I were to go Kimber Montana and wanted those ballistics you could get a heck of a lightweight hunting rig in Kimber Montanta 84m and the 7-08 round. Kicks like a kitten and offers great bullet ballistic coefficients.