Bartlein #3, possibly a #2b would get you a light stiff barrel.
I have a #3 at 18" in 308 Winchester that is 8.4lbs with with a McMillan Game Scout, a 5/8-24 Terminator T2 brake, a 23oz optic and steel mounts. It's handy and fits the bill for my original intent. Shoulder measures .740" at the brake.
