Update.
After a lot of messing around (isn't it always the way) I finally determined that my "known working" FTDI cable is in fact not transmitting correctly.
I did manage to figure out the Nextion Editor. It's actually a simple concept presented in the most confusing way possible (and with "chinenglish" instructions). So I made myself a button that just transmits a "hello" message, and I can see it on a serial monitor! But sending data the other way - nothing...
So, find my backup FTDI connector, and spend a few hours sorting out Windows driver conflicts, and now it works!
I can actually upload from the editor, debug with the display connected, and upload via a python script.
Now back to the mcThings module.
More problems. It seems the "you can define any pin as anything" theory is not quite so much. Only pins 0 to 8 are defined as pins, the other pins are "allocated" to specific other things. The pins I wired (not sure why I wired it this way) 9 and 10 are allocated to the Green and Red LED. So I have to allocate the UART to RedLed and GreenLed - you can't rename them, or allocate them as inputs/outputs, despite what the documentation says.
It is all a bit baffling, and doesn't work. I may have to rewire, as I suspect the LEDs are defined as outputs, and I can't change them.
So progress in that the display is tested and working (and I understand the editor a bit better now).
Stuck in that the pin allocations on the module are confusing.
Will break out the soldering iron tomorrow. I have scored some rare-as-hens-teeth 0.05" headers, plus a difficult-to-find 0.05" to 0.1" adapter board, so I was going to wire one of these anyway.