Thanks for sharing your son's story! People on the Den are super helpful and I'm sure they will find a way to source the thermostat housing.
First off, sounds like you're in the Denver area - so am I, along with several other Eagle owners on the Den. We used to try to get everybody together every once in awhile to talk Eagles but it has been a couple years now. Also, if you are into Eagles, and AMCs, we'll have to arrange a trip to the Rambler Ranch, near Elizabeth. Terry, the owner, has what must be the largest collection of AMCs, Ramblers, Nashes, etc, and is a great host.
Since you are dealing with the Iron Duke motor, would the part you need also be on the GM version of the engine? Denver has several junkyards that have their inventories online, and that could be a source if you check there weekly. Let me know if you need the links to these yards.
Good luck, I'm sure the Eagle community will get your son's car back on the road!