I've built a couple of the 6.5 WSM now. What you are wanting to do is going to be tough. The 6.5 bullets are so long compared to others.
Even with a Wyatt's extended mag in a Rem. you would be seating the bullets really deep.
As much as I hate to admit it, Savage is one of the biggest SA and might be a little better than the Rem.
I don't suggest a Win. The lock time is just too slow for a 6.5 WSM. They have some definite ignition issues.
I still think that to fit in any SA mag, you might want to go to lighter, say 120grainers, without cutting into your case capacity.
The factory 300 even fits best with 150ish bullets. It really needs a medium action.
If you really want to stick with the heavy bullets, put it in a LA. Built a ton of 300 WSM
in LA for guys shooting 190-210 in it.
Let me know, I can help you out with bullet selection, loads, etc. or even building it for you.