About 3000 miles out of the way, but Amelia Reid Aviation at Reid-Hillview near San Jose, CA rent taildraggers. They have no Cubs, but have Citabrias Taylorcraft and Aeroncas. OK, so it's a long way extra to travel, but it proves these aircraft can still be found if you look around. Flights to the west coast can be had quite (relatively) cheaply and the flying out there's MUCH more interesting and varied than Florida (I just got back from 5 days flying out that way).
Oh, and in answer to your other question, everyone I've every rented from by the day has required a 3 hour minimum for each 24 hour period. I've heard of others asking for 4 - especially at weekends.
Good luck, and Email me if you need more info.