Alright. Got that fixed up, changed my APN and now I have a true Global IP address in the 14.x.x.x range.
Anyone with any more ideas, I’m all ears. 
Right, so an update to anyone who might come across this thread in the future, or persons who are curious - I gave up and bought a mobile router/hotspot that had uPnP/port forwarding capability. As with many things in life, throw enough money at a problem, and it will be solved. I’m no longer getting NAT problems, and matchmaking is working fine on the Switch. https://www.amazon.co.uk/d/Networking-Devices/TP-LINK-M7300-LTE-Advanced-Hotspot-Supports/B01BVTM5JW
Now, I’m still rather annoyed because there’s no technical reason why a mobile phone hotspot would be unable to perform the same function, but I’ve made my peace with that. Also, be careful of which mobile router you get - some of them don’t actually have uPnP/port forwarding functions either.