What do you mean catching on the edge of the barrel? When you try to chamber a round from the magazine? Or are they seated out too far and contacting the rifling when you chamber them single shot?

I have a 375-06 AI on a 1917 action and don't have any problems loading from the magazine.

I would expect the Savage design to have trouble feeding flat nose bullets (no cone on chamber face, no ramp). Heck my 221 and 223 Savages don't like to feed some HP designs.

350's are a little long for the 375-06 AI anyway.