So after a lot of reading on the zimbra forums, going over the error messages in the log and some futzing around with the URL format I figured it out. In case anyone needs to sync with Zimbra email platforms, what it came down to was using %40 in place of the @ symbol. I saw it in the log, so I thought why not try it in the URL string, and it worked.
The standard WebDAV URL for Zimbra is: https://ZIMBRA-SERVER/dav/USER@DOMAIN/Briefcase/Joplin
But what worked with no errors: https://ZIMBRA-SERVER/dav/USER%40DOMAIN/Briefcase/Joplin