I'm aware of a couple Savages converted to .35 Remington and they went with new barrels because of chamber issues. A pre-1960 Savage action won't cut the mustard for .356. Sounds like a good opportunity to build a.35/.303 wildcat. Keep after JES.

"You can lead a man to logic, but you cannot make him think." Joe Harz
"Always certain, often right." Keith McCafferty