I don't believe the current JFBCInvite module can forward to a Facebook Page. I'll have to look into it more, but I'm pretty sure Facebook only allows us to forward to the a page on website the specified in your application.
We're investigating upgrading to the new Requests 2.0 system, which will allow invites like you're mentioning, but this won't be until the 4.1 release (4.0 is scheduled for later this month).
As for 4.0 though, we'll have some cool features for Pages, where you can show your website (or certain pages of it) on your Page itself. In addition, we've implemented Peel Page functionality, where you can show a specific article to user's who haven't Like'd your page.. and it won't let them continue to the rest of your site without Liking the FB page first.
So, at the end of this month, hopefully we'll be able to help you get more Like's for your Page, like you're looking for, but it won't be directly through invites. For the next big release, we're already shooting for an improved/overhauled/revised invitation system that, when combined, may do everything you're looking for.
Hope this helps, and if you have any other questions, just let us know!