No, not really. The Remmy and Savage are just barely capable of dealing with the forces involved. If all you want is a gun in the safe that is a 338LM and run a few boxes of ammo through it, they are fine. But if you want to shoot the thing day in and day out............
Much better at this level of "gun" is to start with an action designed to deal with the forces involved {BAT, Lawton, a few others}, and build the gun from there. You are going to want a breach barrel diameter of 1.30-1.35"; 4 inches long, tapering to 0.92 at 27-28" at the muzzle.
Also note: shooting a 338 LM is like lighting cigars with $10 bills, $4 if you reload.