I fitted an 8 gallon wing tank to my L4H and that gave me a bladder bursting 5 hour endurance which gave me a 350 mile range in still air!
The Cub is a lovely aeroplane but with hindsight I would have gone for a Champ which addressed all of the J3 / L4's faults: 10 mph faster on same hp, flown from the front seat, decent undercarriage, easier access. All with the added bonus of being the same cost to run and cheaper to buy!
There are a few Austers and their Taylorcraft cousins out there that significantly out perform the Cub and still retian the 1930's chic.