Referral Form with Multiple Referrals

I've been digging around to figure out how to handle a multi-part referral form. The basic flow is:

1. A partner/referrer fills out a form with their information
2. They then fill out a form with the information of the propect/referred-person, pre-populating a hidden field with the email address provided in Step 1 so that they get credit for the referral
3. They have the option to go back to #2 and repeat the process

Having cobbled together a solution, I have the second form set up using this solution:

<script>
//add a callback to the first ready form on the page
MktoForms2.whenReady( function(form){ 
	//add the tracking field to be submitted
        form.addHiddenFields({"_mkt_trk":""});
        //clear the value during the onSubmit event to prevent tracking association
	form.onSubmit( function(form){
		form.vals({"_mkt_trk":""}); 
	})
})
</script>‍‍‍‍‍‍‍‍‍‍‍

(Cribbed from https://developers.marketo.com/blog/clearing-marketo-tracking-cookie-from-forms-2-0-submission/ )

This works insofar as I end up with two separate people in Marketo's database - one from each form. But what I've found is that the second form still seems to set a new cookie on the person, so the confirmation page visit is attributed to the referred prospect, as opposed to the partner initiating the referral.

How can I keep the tracking cookie from Step 1 intact throughout this process and never set one during Step 2?