How can I send POST data to the JotForm page itself, not to the thank you page?

I want to recreate this form in JotForm: http://bellevuerotary.net/icecreamsales/

It has a sign-up spot for every shift. After you enter your name, etc., and click submit, your name instantly appears in the list under names, so everyone can see who has already signed up for that shift. Feel free to test it out. 

I read through this information: http://www.jotform.com/help/213-Send-POST-Data-From-JotForm-Using-PHP-in-Custom-Thank-You-Page

I don't want to us a Thank You page, though, and it also looks like that is only going to work on a single submittal on a form, where I have many submit buttons. People can sign up for any number of shifts. 

If there is a better way to do this, I'm all ears, but we do need to show the names on the same page like it is now. People want to see who is already working a shift. In addition, this forms write the results to an admin page where everyone is listed, and names can be deleted or changed if, for example, someone cancels their shift.

Also, I tried to import the form and it said "Form not found: Form Id is missing or irregular." 

Is this possible? Am I asking too much?

What you have described is actually a complete system in itself - not only a form.

You would use a form to submit data to such system and leave the tracking, editing, monitoring and such to the system.

While it would be possible to create a simple system which interface would base itself on a single form it would require some custom codding on both server side and client side and that is something that is not possible to do with a jotform.

What I would advise is to find a developer that would create such system for you as that would allow you to have all of the functions that you are after. Once you do, it is easy to set up webhooks or a form to send POST data to the endpoint that will add the new entries to your new system.

Alternatively you could also capture the data over the form and pass it to your website to save and show it in the listing - would that work for you?

You're right, it is a system of it's own, and I did have help from a developer getting it set up about six years ago, in an app called Freeway. I was hoping to adapt it to JotForm and use it in the current WordPress site, but I guess it would be a waste not to use the system that is already working and to try to reinvent the wheel with JotForm.

I ended up recreating the page in an HTML editor, still using the same system. Thank you for your quick response. At some point, I would like to investigate JotForms webhooks to maximize my use of JotForm. I feel like I've barely scratched the surface.