I put a 7-300 WSM prefit Remage barrel on my rifle this year, it's by far the most ridiculously accurate rifle I've ever shot..
I'm getting 1/2" groups at 200 yards with 180 ELD-m's @3000 FPS, just shot a Muley buck at 430 yards with that bullet and it put him in the dirt hard.
I just worked up a load with RL26 and 195's @2925, haven't been able to test it at range yet but I'm excited about the velocity.
I went 7-300 wsm because 270 winchester brass is super easy to find, and all I have to do is run it through a .284 expander mandrel and shoot.
If you're not scared of Hornady brass the 7 WSM would be my recommendation.
Since you're doing things right with your build I would really stay away from belted magnums.
I've had case sizing issues in the past with a 7mm rem mag, and accuracy wasn't near what I'm getting from the WSM case.
Good luck with whatever you choose, 7 mm's with heavies are awesome.
Great long range performance, and easy recoiling in a lighter setup.