Terminate connection to jQuery AJAX request, keep processing php on server side?

I have a signup form that calls a PHP script which can interact with our CRM's API, like so:

CRM API <--> PHP script <--> Signup form

1. The signup form passes some information to the PHP script in one AJAX call
2. The PHP script run a dozen API calls to the CRM to create an account and attach various data
3. The CRM returns the new account id it just created to the PHP script
4. The PHP script passes the account id back to the signup form, at which point the AJAX call is complete and the signup form can continue.

The problem is #2, those dozen calls take about 20 seconds to complete, but the data the signup form needs is generated after the first API call so it could in theory return that data much sooner and do the rest of the stuff server side without holding that AJAX call open the whole time.

I tried flush() and ob_flush() which does output account id to the client before processing is complete, but the jQuery AJAX connection remains open so I'm still stuck waiting for the connection to be closed on the signup form side before anything happens.

So what's the easiest route for returning that account id to the form as fast as possible?

Maybe break out using curl and exec?

 if(signing up){
      stuff
      exec(curl myself, notsignup)
 }
 else {
      bunch of api calls
 }