Update (to help any non-Captains if they have the same issue in the future) :
I finally got through the phone this morning. There was an additional payment due, but I was never contacted despite Uniden having my phone and e-mail. Also the online notes never reflected any payment due, just the notation "IN LINE TO BE SHIPPED," and an estimated ship date 2 weeks ago.
Uniden's repair service itself is the best I've ever encountered with an electronics firm, but just a suggestion to UPman: the long wait times may be due to the fact that people have to call in to get this info, and its not reflected on the online status. I never got a postcard, never notified by email or phone.
If payment is due, customer could be sent an email (or at least posted online) and allow for payment via the web.
Thanks to everyone or their help.