Well! Finally, after three attempts, I successfully installed the Adafruit WebIDE by following their instructions here:

Overview | Adafruit Learning System Raspberry Pi WebIDE | Adafruit Learning System.

One thing to note. the instructions are currently wrong. The IDE does NOT start on port 3000, it defaults to port 80. To change this (as I had to), you need to edit the following file:

/usr/share/adafruit/webide/config/config.js

and change the obvious line from 80 to the port you want. I actually changed it to 3000, just to keep continuity with the mistaken instructions.

Should be interesting to try and use it in anger in the next few days when I’m over at my parents and have some free time.