The pellet gun story reminds me of what I was told by a pellet gun repair person.
He disassembled the weapon, and used a hydralic press. He inserted short sections of rod, and pushed them gentilly in series. He therefore went slowly, with a gentle force, and never had to worry about any misallingment. Ther was never any "impact." The plug touching the projectile would be the only one that needed to be near bore size. Put a wrap of duct tape around rod section diamiters: just make certain the rod used is metal.
Build on this idea for your circumstance. The press opening would only need be slightly more than your barrel/action length.