selkirks method of heating the tires up sounds like it would make it easier to put back on, but once you get it back on it would be nice to figure out a way to keep it from rolling off again. Woodlandfarms mentioned that his had a hollow core, I don't know if mine is like that or not.
I don't know if this would be a solution to the problems with your tires rolling off the rim or not, but I was wondering if you could get two metal rings for each tire, have a hole in the center of the rings a little larger than the rims and have the outer side of the ring smaller than the outer circumference of the tire and drill mating holes through these rings and then maybe drill holes through the tires to match the holes and then bolt the rings on the tires. I don't know about drilling holes through the rubber tires though if that would be possible. Seems like I have seen racing slicks with the tires bolted to the rims to keep the rim from slipping inside the tire, maybe someone else might have a better idea, hope so.