Just to close the loop on this, in the end I exported my data to .jex, and imported it into a new profile.
The new profile is configured to sync using WebDAV, and not only have I left those pesky (and distracting!) error messages behind, but the sync process is now much faster.
With 20/20 hindsight, doing this took next to no time, and unless I was actually missing data I would do this rather than try to troubleshoot next time around.
I hope that helps anyone else who finds themselves in this situation.