How can I get Thunderbird Contacts to sync with Ubuntu One on Ubuntu 12.10 Quantal?
You cannot. It appears evolution-couchdb (and thus the Thunderbird extension which depended upon it) has been removed; likely due to API changes in upstream evolution-data-server, and no resources to update the plug-ins.
It's also worth noting that it was announced in November 2011 that desktopcouch/couchdb support would gradually removed from Ubuntu One. However, replacement infrastructure is being worked on in the form of u1db to replace the pieces which couchdb was being used for.