Well, if that rifle is going to weigh ten pounds, you might as well go for the .300 WSM.
I shot a Model 70 Winchester Classic in .300 WSM and witht he scope that was on it, the gun didn't seem to kick any more than my 30-06. I'd estimate the weight on that M70 to be about nine pounds.
You'd have more bullet choices in the .300 than there are in .270 caliber too.
Being the single shot nut that I am, the .300 WSM is the one I would pick if I were in the market for another .300 magnum. Right now, I have two Ruger #1's, a #1b and a #1S. They're lighter than your planned rifle and recoil isn't all that bad with them.
Paul B.