Set default form values after AJAX callback
I finally found a way to do this, though it appears this isn't the best way to do it - but it works. 

You can not set #default_value for a field if the field is set in $form_state['input']['field_name'].

So before I try to set the field to the newly generated value, if I put this before then I can reset the default value. 

unset($form_state['input']['registration_information'][$name][$subname]['field_name']);