Well, I am by no means a tub veteran. In fact, I recently switched and had some of the same problems you are having. First off, 120 on the surface of the plastic is wayyy to hot. Chances are the snake will wiggle its way through the substrate and get burned. I believe you want the tub surface to be 92-94 and have a thin layer of substrate(which you said you have). It doesn't matter if the top of the substrate is in the 80s cause the snake will be able to find the heat if it needs to.

Now your cool side is too cool because your room is too cool. My house is ~70 all the time. I had to buy a space heater setup and stick all my snakes in the closet which stays around 80-83 now and works great!