Christian,
Sorry for not getting back sooner. Your question was immature or incorrect to make, it just takes time to think about responses to features we don't currently offer.
Your plan of attack sounds correct. JFBConnect definitely takes care of the 'core' Joomla/Facebook integration.. creating users, storing keys, etc. We have a lot of other functionality on top of that, of course, but what you're looking for isn't one of them. The jfbconnect.js file uses the FB.ui dialog for sending App Requests, and may help see how we use it, in addition to Facebook's examples. I'm assuming you know Joomla a bit too, but if not, the Requests functionality can show you how to mix the Javascript and PHP/Joomla calls to create enhanced functionality.
The multi-friend-selector your looking at also seems appropriate from what you describe, though it ends up using the 'apprequests' FB.ui call, which is what we also use for our Requests logic. The example on that page, for the checkboxes, is just a way to fully customize the Request form instead of using the built-in one that Facebook offers. Either works though. I really think the Requests functionality we have may be a good starting point:
1) Create a request in JFBConnect: "Create your group"
2) Let user's send that request
3) JFBConnect will track the requests automatically
4) As (or after) a user registers using Facebook, you can see if they were previously invited by someone. If so, give that user credit, or put the new user in a special group, or whatever.
If you have any questions on what we've done, or why, don't hesitate to ask. I'll gladly help you try to do what you're looking for!
Best of luck,
Alex