1) If the live mouse is an appropriate size, I would go ahead and offer it. You may have better luck if you don't hover, and turn the lights off.
2) Those analog gauges are notoriously inaccurate, so you are right to get rid of it. The other issue is that the gauge isn't measuring the temperature at the same location as the thermostat probe, or even in a location where the snake actually is. You don't really need to know what the temperature is along the glass a few inches up in the air. That isn't where the snake is likely to be. You need to know the temperature on the cage floor where the snake actually is, on both the warm and cool sides.
3)The thermostat you have can work, but it isn't all that accurate either. So you really need a good thermometer to verify what your temps are. You may find that having that thermostat set at 89 doesn't actually give you an 89 degree temperature. It may take some tweaking to get everything right. Partially, it is because that thermostat has temperature settings that are not all that precise and partially it is because it is an on/off thermostat that doesn't check the temperature all that often. So your heat sources may be heating things up quickly and the thermostat may not be keeping up, if that makes sense.

I am curious to see what the temps actually are...I am guessing they are higher than you think.