Hi,
Try and dial it down to keep the top temp inside the warm hide around 93-95 if you can as too high a temp can be dangerous and it's a good idea to keep a nice "buffer zone".
Also measure the temps on the glass directly above the UTH and make sure they are about the same - there is no way to predict when your snake will burrow down.
What are the temps on the cool side?
It might be a better idea to move the heat lamp into the middle so it heats the whole tank and keeps the cool end at 80-82f and let the UTH on the warm side keep it around 93f. It depends what the temp range on the tank is really.
Another thing to think about - I have a cool house (sadly only temperature wise) so I actually put aquarium backing round the back and sides for appearance but then covered that with a layer of insulation to help keep the temps more stable. I chose to use cork sheeting as it looked nice and was easily available but there is also bubble wrap and foil stuff - I think it's called reflectix that may actually insulate better.
What are you using to control the heaters?
It's all about problem avoidance when setting up enclosures - if there are never any dangerous hot spots or tape in the enclosure he can never burn himself or get covered in glue.
And yes it is perfectly fine to simply spread out newspaper on the bottom of the tank (with the temp proviso above) - I generally use at least two layers of newspaper as they do pee a lot.
And I agree on removing the reptile carpet too.
dr del