Your research is correct. Honestly, the only way to use a heat pad on any surface (glass, plastic, PVC, etc) is with a thermostat. Without a thermostat they simply get too hot for a BP and will cause burns.
My other recommendation is to not actually stick the heat pad to the tub itself. Use foil tape to cover the surface of the heat pad so that it can be moved easily whenever need be (sticky side to sticky side).