Just to answer my own question, I think I've found a solution!
I have upgraded to 10.13.6 (took a full backup first) and the eGPU is working lovely now.
I installed the 4.3b5 DisplayLink driver and I can now use the internal screen plus 1 over Airplay (seems fine so far, but haven't used it much yet).
My USB->HDMI adapter only works in clone mode with MacOS - probably explains why it was in the bottom of my laptop bag, but I have a USB-C to Mini Display Port adapter I've been using for ages and that works fine. It gives me two external screens and the internal screen. All in extended mode.
It's a bit like dongle heaven with all these cables sticking out but at least it works and means I can continue to use the D3100 dock for now. It's not the triple screen setup that I always used to use but thats been so troublesome over the years I had pretty much resolved to go down to two external screens anyway.
I just need to go and make sure that the DisplayLink driver doesn't interfere in any way with Apples eGPU setup.
Forgot to add the adapter link:
https://www.amazon.co.uk/Benfei-Disp.../dp/B06W53PXRB
It's not flawless, sometimes I have to connect it a few times before the monitor wakes up but once it's away it works great. I suspect you could just use a USB-C to DP cable instead?