How about decoupling post-invite functionality and leaving it to Rules or other modules, exposing appropriate hooks on invite create and invite usage events?
So the main purpose of the module becomes generating unique invite URLS and just take care of their usage tracking, so users of the modules can decide themselves what actions to trigger after invite link is used by invitee. This is an idea that rises from our particular use case of course (we completely replaced Drupal's standard User registration on one of our projects), but there might be other use cases where hardcoded redirect to user page might not work.

If you are interested in going this direction, we can join forces and help with development of the module.