Have you tried out a bicycle with an internal hub gear? I don't know how loud they are, but you shouldn't have any chain binding issues (and you could probably run a belt if you wanted).
Oh man, I had a Ghost bike with a Continental drive belt that was a constant pain in my ass until the belt snapped at 1500 miles and practically chucked me in front of traffic.
REI really stepped up and Ghost warrantied the entire drive system as the Continental system was NLA; they replaced the whole thing with a Gates Drive system which is amazing.