Thank you so much, I'll definitely try out the plastic. My dad works a lot with construction and I've heard some good things about plexiglass, so I may ask him to help my cut out a top to cover it. I ordered a digital hygrometer so hopefully that should be arriving soon and giving me a bit more accuracy in the readings.
The CHE isn't on a thermostat, but it is on a dimmer set to a pretty low setting which keeps the ambient temps ~79-80 degrees from the 75 my house usually is set at. I've been checking the temps and everything pretty obsessively. If I notice that she's getting curious about that area though I'll probably end up figuring out the clamp, because I don't want her getting burned. Out of curiosity, my uth is hooked up to a thermostat--would things get funky if there were two separate thermostats running two different heating elements?