I'm not sure where you are using the form. If it is at registration, I think you could use the Pageroute module to force users through a series of nodes that call uc_addresses_new_address() with the hook_menu function uc_addresses_menu(). This would mean that you do not need to override the submit button. I'm not sure how your Drupal install is setup, but on mine, you have to enter a username and email, then click submit. When you get your password from your email, you could login and then be forced to enter your address info with the Pageroute module. It sounds like you might be trying to alter the registration form by adding the address form there.
http://localhost/user/register

With pageroute, you should be able to turn registration into a 2 node process. One for the username/email and one for the address form.