So, after unplugging in the device so I can bring it upstairs to debug it, things have started working ....
Turns out, for some unknown reason, a reboot (of the device) was needed, even though they worked just fine in the app. My own REST calls via Paw (Postman-like), have started working, too!
There was definitely something "buggered" on the devices. I had to boot both of them, and they now work!