So, I've managed to fix the problem of not being able to transfer music, by using my hotspot instead of Wi-Fi - I'm not sure how much data I'm using by only ever being connected to my phone, but that's another question!
But now I have another problem: I can't delete or re-install the downloads that failed when I was trying to transfer over Wi-Fi. If I go to my library and click 'Remove', it goes to the 'music syncing' screen and shows me the percentage that had downloaded before it failed, then it doesn't do anything else. Any ideas? After a decade of Garmin watches I'm getting very close to getting a refund on this and buying an Apple Watch...