How does the 7rem mag shoot now? As a hunting rifle, a heavy barrel isn't necessary. I don't intend to fill the air with lead at my game. Usually, one or two is all I need and any sporter barrel will handle that.
Ballistically, the 7RM is head and shoulders above the 308. Wind drift, retained vel, etc are all much better. When hunting, we can't control the conditions so anything that can help me get the bullet to the boiler room is a must have. High BC bullets is a great start.
If recoil is an issue, a muzzle brake
can be added.
The are so many awesome bullets in 7mm to meet your needs. Start there. You can always switch if you need to. I doubt you will.
Compare wind drift and retained vel/energy of a 162gr AMax/SST (BC 0.65) in 7mm going 3000fps with a 175gr 30 cal MK going 2600fps (BC 0.55). Big difference.