Creating a Searchable Calendar Site that Users can manage

So here’s the thing. I’m building a site for a client and I’m trying to figure out the best way to go about this with WordPress.

It’s a public calendar, where anyone can register and submit events. There is a form for the events submission with various questions and information, and then those submissions would get approved, and posted to the live site. Later a user who has registered could go back in and edit the event they posted.

I’ve started using Gravity Forms trying to make this site work. I added Gravity Forms + Custom Post Types which should allow me to make the submissions from it turn into a custom post type, since that would be easy for me to manage, and would be searchable. But would that allow people to go back in and edit the submissions later? I’m not sure. And that’s a really important piece.

Does anyone have any suggestions or better ways of doing this?