Not wanting to download all those assets again, I was going to copy them over from my Windows installation.
Then I realised that I don't have TF2 installed on Windows at the moment. So I tried restoring my backup of my Windows install to my Linux Steam instance.
Well, it wasn't a total disaster... it had a try. So far it's still stuck at the "Validating - 100%" phase, like it has been for about 10 minutes. I may just kill it and reboot to Windows and do it there.
The download is now stuck at "Paused".
Ah well, it was worth a try. I'm guessing the 9% I seem to have accumulated probably got downloaded while I was waiting. It was probably too old a backup anyway.