Why do you have a probe maintaining the cool side? Since the heat tape gets really hot (as you know) use the thermostat to regulate the heat on the hot side and let the cold side be. You say your reptile room is 74 degrees, which is cool but I think bin your case too hot is worse than too cold. It's fine to monitor the cold side and I've heard some people putting a extra small layer of heat tape on that side to regulate it.

When your using your thermostat probe on the hot end to monitor your cold side there is a couple problems I see.
1) The heat coming off the heat tape is far away from where you're measuring it. It takes time to heat up air and by the time the probe reads good on the cold end, the heat tape will be hot as balls on the other end which is bad for the snake.
2) balls aren't as dum as some people seem to make them out to be. If a ball wants to be 80 degrees, there will be a spot in the tub that's 80. Like for instance, of the hot end is 90 and the cold end is 70, it's logical that halfway between is 80. The ball will go there of he or she needs too.

I think your worrying too much about the coldness of the cool side and not enough about the hotness of the hot side. Hope what I said makes sense and helps.