A longer scope would fit, or just buy extension rings.
Looking at the American I have a hard time believing you'd have a hard time making almost any scope work. A long action Savage is the only gun I've ever had the slightest problem with.
I could be wrong, but my 1st thought is that the guy at Dick's was clueless. I still think either of those scopes should work with standard rings. Neither is an especially short tubed scope.