Are they gauges or digital? Gauges aren't necessarily accurate all the time. I like using digital thermometers with probes to tell my temps. If it's cold in your house that can be a factor of the cool temperatures.
You don't have to take the heat lamp off, cover 2/3 of the lid with saran wrap or plexiglass so the humidity doesn't escape as much. You'd probably be misting the enclosure once or twice a day to maintain good humidity.
What you can do is buy a plastic Sterilite, Rubbermaid, or Iris tub that can fit the snake along with their hides and dish.
You can drill holes around the sides until you can get the humidity where you want it.
Then you can attach a UTH underneath the tub (on one side only, let it cover only 1/3 of the bottom of the tub) with some aluminum/foil tape. Duct tape isn't very good to use.
Make sure the UTH is controlled by a thermostat. Uncontrolled UTHs can get about 130F and cause severe burns on your snake or overheating which can kill it. Either way you may not have a good ending if that UTH gets too hot.
Tubs work great for keeping humidity and you can control your temps a lot better (plus they are very light weight!). Make sure you've got a digital thermometer with a probe (Accurites work very well and can tell cool side, warm side, and humidity) to put on the bottom of the tub underneath the substrate right where the UTH is.