I found the logfile. I had configured the log directory to be "~/.config/syncevolution/google/log". Apparently Syncevolution took that literally, creating a ~ directory in whatever directory I started the sync from. Changing it to an absolute path solved that problem.

Trying to sync a bunch of times solved the other problem. It still gave me the errors, but finally made a successful sync.

Also, running Syncevolution with my settings creates backups before and after each sync, containing one vcard file for each contact. Doing that with a large contact list will eat up your space after a bunch of syncs, even if df and such says there's space left. I guess it has something to do with inodes and number of files etc. To get back in business, delete the backups when not needed any more, or tar'em up.