How can I keep my jam from overcooking while I process it?
If it's getting cooked too much, well, stop cooking it. You can cover it to prevent water loss. If it's too hot sitting on the same burner (on an electric stove), move the pot. It sounds like your cast-iron pot might be part of the problem, too - if it's still staying too hot, you could pour it into something else. Finally, if you do still have significant water loss, I believe you should be able to add a little water (careful not to add too much) and stir and reheat.

P.S. you could also just get a lighter pot. (I know that's not ideal.)