Dovecot (with Postfix) configuration has connection refused when accessing auth-userdb

The connection refused error is indeed the problem. Connection refused on unix sockets is not terribly intuitive, but it indicates that there is nothing listening on the socket (typically, the process is dead, or the file given as the address wasn't a socket at all). This should never be a permissions issue, unless dovecot is unable to open the socket for listening due to permissions.

Try stopping dovecot and postfix, removing the socket file at /var/run/dovecot/auth-userdb, and starting postfix and dovecot again (ensuring the user dovecot is running as has permissions on /var/run/dovecot). Usually this will fix this type of issue.

Netstat will also display unix domain sockets. Check its output (use netstat -nvlap | less and search for the path or for dovecot) to ensure dovecot is listening.