Well looks like this'll be another learning experience then, I've never done heater work but I've had to repair a few a/cs. I did watch a video on how to replace the heater core in a same year Towncar, it definitely looks rather involved but should be manageable. That 13mm mod is pretty ingenious.
I found a 12v portable heater under the passenger seat, neat little thing, I've never seen one before, I tested it and it still works. It may come in handy if it gets cold before I get the heater situated: