Savage 24?
Don't know if this has been mentioned, but it might be worth looking for an old Savage 24V or 24F. I've got one of each. The 24V is .223 over 20 gauge while the 24F is .223 over 12 gauge. The older 24V is my favorite of the two. The rifle barrels on both are quite accurate, though the 24F appears and is (since new) rather rough inside. Patterns from the shotgun barrels aren't the best, but good enough for squirrels.
FWIW, I think the ideal squirrel rifle would be the Savage 24 in .22RF over 20 gauge. .22/.410 Ga. would be good too. Been awhile since they made those, but there's always a few at the gunshows.