You need a thermostat for your UTH (this is an inexpensive option). The glass above the UTH should NEVER get hot enough to burn your snake. The thermostat regulates your UTH and keeps it a proper, safe temperature.
Removing some cypress will help the UTH get more heat into the cage, but UTHs aren't designed to heat the ambient air. AFTER you get the thermostat, cover three sides of the tank with insulating foam/cardboard/etc to help retain heat. You may need to get a higher wattage bulb, which you can regulate with a lamp dimmer.