First and foremost, get that bulb on a thermostat. All heating systems need to be on a thermostat, always.
Personally, I don't do feedings when the snakes are in shed. My BPs go through the cycle pretty quickly anyway, a matter of days. They shed and poop, often enough inside the shed. I find it, clean up, and then feed.
The snake is eating so things are going generally well, but you might want to put more thought into your heating system.
Don't you find two heat sources needlessly complicated? Why have two thermostats when just one will do the trick? Plus there's the issue of a glaring 60w bulb. You need to run the thing 24/7, its going to blow out, the snake is nocturnal and likely isn't in love with it. I would really look for another option.
Here's a quick and inexpensive fix. Unplug the UTH, get a ceramic heat emitter (CHE), reposition the stat probe inside the tank, and plug the CHE into the thermostat. Your temp issue will disappear in hours.
Just a thought.