Your issue with the thermometer reading differently is caused by having one directly under that heat lamp. The heat is coming straight down on that one so you're seeing a higher temp and a lower humidity. Think of it this way, if I hold a hot dog next to a campfire it won't cook as quickly has if I hold it over a camp fire. Your thermometer on the wall is catching ambient heat, your one on the ground is getting direct heart.
I don't entirely agree with this advice. Belly heat, aka heat generated by a UTH or heat tape, does next to nothing for ambient temperatures in the enclosure. I've also never seen anyone using a bedsheet to hold in heat and humidity. Not saying it's not possible, but the duct tape + aluminum foil method has never failed me. Regardless I wouldn't recommend getting rid of the overhead heat when OP said that room gets pretty cold. If you want to do away with the light generating heat lamp, a ceramic heat emitter is a great option, but I think you'll find many keepers here that have kept snakes under some type of nighttime bulb with no issues.