Don't put your thermostat probe in the enclosure. Keep it outside. Some people keep their probes successfully inside, but I wouldn't risk it. The snake could move it off the heating source and create temp spikes.
If it says 98/108 degrees, then the Thermostat shouldn't even be on if it's set to a max of 93. Could your bulbs be making it too hot as well?
As for which to trust more, Hydrofarm or Accurite. Neither. Both aren't very accurate. And the thermostat isn't meant to be used as a thermometer. I've had 4 Accurites and 2 of them were 10 degrees off from one another. The remaining two matched up with my temp gun.
I would invest in a temp gun.