it's possible the starter is wearing out, but make sure all your connections are 100% with heavy enough cables before anything, especially as you've just changed engines - and consider if this 'never started' engine may have other problems ... yes, the stomp starter '55-'60 was 12V, but if you switch to a 12V starter, you'll need to change the flywheel/ring gear, as the later 12V starters had a different tooth count, although the shop may be able to change yours to 12V with a rebuild - if it needs a rebuild
Bill