That is a good idea and worth a try, but it takes more powder to get the
bullet up to speed over something like a 308.
Still probably only about 2# difference in recoil.

I would probably try a reduced load with Barnes 130 gr TTSX, bullets and weight a duromax stock with 1 or 2 mercury recoil reducers
to about 9# total.

A 130 TTSX should drop most any animal with a good shot.

60-65 gr of H4895 should push a bullet to around 2900 FPS and in a 9# rifle total weight the recoil would be about 15#.
Minimum opening speed for that bullet is probably about 1600 fps.

1000 fpe limit would be about 400 yds.
1600 fps limit would be about 550 yards with 760 fpe.

I load that bullet in a reduced load for my Dad who is 90YO in 30-06 at about 2600.