Thanks for your help so far. I can now get my brawler variant to load correctly, but other variants do not.
I don't think it's a problem with the variant file. If I copy the same variant file but give it a different name (and add this name to the fleet sheet) it will not show up. This happens with core variants, too - they work fine and will load correctly, but if I change their name they will not load.
EDIT - I needed to change the Variant ID tags within the variant files. Sorted now
What was making things difficult is that I didn't realise changes made to the variants needed me to reload the game to take effect. I did fix the variant tags, but I didn't reload the game.