1. I would get the hot spot temps down. Regurgitation could be because hot spot is too hot and he didn't use it. It can also be because prey item is too big. What size rat? I know you said rat pup (but don't remember weight off the top of my head). If similar size to mouse, he probably should not have regurgitated.
Some BP's will not switch to rats, but most do.
2. 70% humidity is ok for shedding, but probably high otherwise. I would aim for 60% average. 70% tops in shed.
I understand wanting him to be beefier before a fast, but what can you do?
Hang in there!