All the parts have arrived. Unfortunately, when I plug in the thermocouple, while I get a correct reference temp of 24.19 °C, I get a nonsensical 1073741760.00 °C as the thermocouple reading. Now, it arrived with a damaged-looking sheath, so maybe the cable is messed up. But maybe not? And this is why I gave this post the title I did. I've done a lot of software debugging in the past, but this is the first time doing hardware debugging. I'm GUESSING that since the reference temperature coming in makes sense for the temp I have the house A/C set for, that the connections between the MKR THERM shield and the MKR WiFi 1010 are fine. I'm also assuming that means the Arduino_MKRTHERM.h that I'm importing is fine.
Of course, it's possible that something is wrong with the inputs on the THERM shield, but unless it's a wiring error on the board, I don't think so because I get the same readings whether I use the screw mounts or the k-couple inputs (although that requires some futzing around since I don't have a k-connector on this wire).
Adafruit was great about an RMA for the wire since (again) it came with what looked like a damaged sheath, but I'm left not yet knowing at this point where the problem lies and how much of an issue this is for my project.
Of course, there's always the possibility of shelling out for some Thermoworks k-couples - https://www.thermoworks.com/TW-113-442-GC then I'd be a lot more certain if the issue persisted that it wasn't with the cable.
That's where hardware debugging is a lot more expensive than software debugging.
But that's why this is where the real making begins....