Re: 6mm Remington
One of the most accurate factory rifles I ever had was a Rem M700 Varmint Special (older wood stocked version) in 6mm Rem. It was amazing!
(I have since built a semi-custom M700 in 6mm Rem, because I was so impressed with my first one...)
As to the stock, yep, it will fit, and should make for a very nice package.
BTW, first post? Welcome!