Overriding Class Div Form-API
See line 398 of plugins/address.inc ? $format['#wrapper_id'] = drupal_html_id('addressfield-wrapper'); That's the root of the seemingly arbitrary field identifier stuff. The code gets there from line 460 of addressfield.module $element += addressfield_generate($address, $settings['format_handlers'], $context);

Make a custom module, set the weight higher than that of addressfield so it runs after the addressfield module's hooks, and alter the form. There aren't hooks inviting you to alter those IDs unique to addressfield, and altering them in this case is no different than any other, so long as the module weight is adjusted.