Hey Chris. Thanks for reaching out here. There was a somewhat-officially supported Gravity Forms hack that Tim Bowen put together a while ago (http://creativeslice.com/tutorials/gravity-forms-events-calendar-submissions/) and which was modified a bit to work with 2.0. Were you ever able to give that a go?
Otherwise you may want to check out our documentation page ( https://theeventscalendar.com/support/documentation ) to see if any of the template tags could be of use. I will note that you could also probably have attendees sign up for events using either our Eventbrite Tickets add-on (where the event could just be ‘Free’ and they RSVP) or Community Events, which allows for frontend event submission.
Hope that helps and sorry I couldn’t offer up more. If you have further questions here let me know.