What is this heat coil you speak of? I'm not clear what it is but I'm gonna say its a safe bet it should not be inside the tank.
A thermometer at the top of the tank is useless. It needs to be a few inches at most from the tank floor. You need to track the temps where the snake is. You should also get a probed thermometer or an IR temp gun to find the hotspot temp.
I'm guessing but with a heat coil and a bulb on the hot side the surface temp is way to hot which is why your snake is staying on the cool side.
Move the thermometer and get another device to measure the hotspot so we can help you better.
As for now I would remove the heat coil and only use the lamp. A lamp alone can provide a warm hide and good ambient temps. A uth is great but should only be used correctly with a tstat. And you should only use a correct uth.
There are other things we can do to insulate the tank and save heat and humidity but we need to know the actually numbers first.
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