Create invoice from Form

Create invoice from Form

I'm looking for a way to create an invoice based off a form. We typically have people register for events and request an invoice. I'd love for the registration form to automatically create an invoice if they don't pay with a credit card during registration.

I have looked into Zapier integration, but the API requires you to set a fixed customer in the integration. Not so useful!

Anybody have a way a form filler can select from a list of customers and pass that into the invoice? I don't really care where the form comes from - Formsite, Gravity Forms, Google Forms, Eventbrite...anything!