How would the rheostat be causing something like this? The thermostat should still be cutting the power when the heat reaches the set point, regardless of anything else in the setup, unless the thermostat has failed. I'm obviously new and you're obviously way more experience, so I don't mean to usurp that authority, but it just doesn't make sense to me.

And, OP, water couldn't "burn" through anything. It would boil before it got hot enough to burn anything except a few choice chemicals. If it's leaking through the holes, it may be exacerbating the electrical problem that's already present.

I vote bad thermostat. How else could you get temperature spikes hot enough to melt plastic?