OP, I don't get your statement about temp swings affecting the thermostat. If you were dealing with a RHEOSTAT (which doesn't measure temp but just controls the output of electricity) I'd be on the same page. I initially had my tank on a rheo but my room is way to drafty- a heat setting that works in the (cold!) morning is too hot for a warmer afternoon which is then too cold for the chilly evenings. At my parents, my old rheo lives on Talis secondary tub and as the location isnt as drafty I can leave it and its ok with minimal babying.
My room-between having a heater on and just chill in the room- can fluctuate in heat a lot. My hot spot, with the probe outside on the pad, doesn't. It will go between 90-92 degrees. The thermostat turns off the pad if it gets too hot and turns it in if it gets to cold. I've never had an issue with the probe getting cold and giving a weird setting.