Shouldn't be a problem as the Remingtons have the "3 rings of steel" around the case head and the bolt lugs will take most of the recoil pressure. When they open up the bolt face, the smith is only taking off a small amount. Consult with your gunsmith to see what he thinks.
I've had it done to Model 70's and Rem 700's and never had a problem.

Bob


Never underestimate your ability to overestimate your ability.