My experiences in the desert do not include 240 lb pilots, but I have had success at Flagstaff, Mountainair NM, Vaughn, NM, and of course Deming, which is only a mile above sea level. In Flag, at 100 degrees and a C-65, I got my altitude by flying south. The Cub is as good as they get on hot, high days, but overloaded aircraft of any type will perform slightly differently at 7000 feet and 95 degrees. That's why the runways up there are two miles long.
Lemme see - a good J-3 weighs about 730# ( unless you are one of those guys who likes to weigh them) and that leaves some 530 or so # for passengers and fuel. Surely 130# of fuel is enough for a reasonable cross-country.
Removing the forward tank in a J-3 is probably one of those things where the cost outweighs the benefits. The wings must be modified, since the PA11 control cables are higher. You won't get any more leg room, since the tank is not the limiting factor; it is the way the forward spars mount.
There really are PA11s out there, and they are not much more than a good J-3. Actually, a good PA18 with a 90-105 HP engine is still under fifty, and there are a few of those left. A buddy just got a 150 HP for fifty, and it had good engine and fabric (no radios, though). Keep the J3 stock, and go get a good Decathlon if you want more interior room and speed. That's what I did.