The oven I intend to use has arrived, along with some heat reflecting high temperature tape.
I set to work on taking it apart so I could install the thermocouple. Turns out there were some pre-existing holes left over from the factory that it threaded through perfectly. Just a bit of the heat tape to secure it in place. Side note: this kind of cheap folded metal construction has lots of sharp edges, be careful!
While I had the oven apart I used the tape to insulate the front glass a bit, as well as some pretty big seams in inner body construction.
Now needs hooking up to my breadboard and solid state relay.