I'm probably out of line here, but I think I would look into moving the the resister to a different location where there may be more, or cooler air flow. If you need to change the pigtail, I would also check into using the old style blower motor resistor in that different location.

The purpose of the blower resistor is to reduce the voltage to the blower motor, and the reason for putting it in the heater box duct work is to help cool it. Nothing says the resister needs to be placed in the heater unit or the heater duct work, just that the blower motor wiring and the switch wiring needs to be connected to it to function. You can leave the dead resister mounted in its original position to plug the hole in the heater box/duct work, just don't connect the wire plug to it, connect the wire plug to the other unit in its new location.

I build hot rods, the blower motor resister on my 49 truck is between the fender and the inner fender where it is kept dry, out of harms way, out of the way where things flammable can't reach it, and has enough air moving past it to keep it cool. The heater box and duct wort are a least 12" away from the resister. Gene