Been there, done that, with a whelen. At something less than 8lb scoped full power 250 grain loads were "enough".
I was tweaking 250 Hornady (2500+) and 225 TSX (2700+) loads this afternoon in a 7#, 12 oz Whelen.
... maybe that explains my headache...
Unless I just wanted to spend more money one of the Ruger Americans in any of the short action calbers will come in under 7 lbs with a Leupold scope. The 7-08 or 308 won't beat you up in a rifle that light. You'll never notice the difference in performance compared to 30-06 which will beat you up in a 7 lb rifle.
I'd also suggest taking a long look at this setup. While I'm certainly a fan of the Marlin X7 bolt guns, the RAR is lighter. I set up a .308 this winter with Weaver rings and a VX1 2-7. I can't decide whether I like most that it's light & points like a setter, that it prints small groups with Federal blue box 150's, or that it was < $400, all-up.
That being said, I'd not dissuade you from considering a Kimber if it's in your budget. A sample of 1 has given me the opinion that their stock design does an excellent job of dealing with recoil for my particular body.
Let us know what you decide on.
FC