I looked through the cyrus-sasl sources, and the only place your original error message ("cannot connect to saslauthd server: Permission denied") is created is when the connect(3) on the "mux" file fails. Note that the error is EPERM, and not ENOENT. Unfortunately there is no logging we can turn on for the SASL client library. Also the perms on the "mux" socket file looks right, and "postfix" user should be able to connect to that file. I am stumped by this as is Bobby.
By any chance do you have selinux enabled or configured enough to get in the way here?
The only other thing I can think of to track this down is configure postfix to launch only one smtpd server, and then make a test connection (so the smtpd process will be up started for you find its pid), strace that pid, and kick off tbird and see why the connect(3) is failing, and more importantly what path the connect(3) is trying to connect to.
See also:
http://www.postfix.org/DEBUG_README.html