Handy online recoil calculator at JBM...
www.jbmballistics.com
With 180 gr bullets at 3000 fps, in a 7lb rifle, that's around 40 ftlbs of recoil. 6lbs would be 45 ftlbs.
That's gonna get you down to ~30 ftlbs with a 168 @ 2900 fps for a 6 pounder. Still substantial.
For comparison, a 9 lb "Grand Pappy's Ought Six" type rifle, e.g. classic wood and metal Rem 700, Win 70, etc, would probably be around 20 ftlbs of recoil. Same rifle in 338 Win Mag would be around 30 ftlbs.
If I was building anything bigger than a 6.5 PRC in a 6-7 lb rifle, I'd put some foam around the scope ocular just in case...