I posted this yesterday, and got a lot of helpful advice that uncovered numerous mistakes I made. I've fixed those, but the problem still persists, so here's an updated version of the question.
I'm trying to set up a Pardot form handler to run from a thank-you page, as is done in this example. I cannot just add the form action with the form handler address like you normally do, as the original form has to send the information to a third-party site. To date, I haven't been able to get that to work at all. I now know my biggest problem was that I was trying to run PHP from an HTML page, which will never work. So I have changed to a PHP page, but it's still not firing.
Here's the code:
<?php
$FirstName = $_POST['FirstName'];
$LastName = $_POST['LastName'];
$Email = $_POST['Email'];
$PayFrequency = $_POST['PayFrequency'];
$Phone = $_POST['Phone'];
$donationAmount = $_POST['donation-amount'];
$MailingStreet = $_POST['MailingStreet'];
$MailingCity = $_POST['MailingCity'];
$MailingState = $_POST['MailingState'];
$MailingPostalCode = $_POST['MailingPostalCode'];
echo '<iframe src="https://go.realurlhere.com?FirstName='.$FirstName.'&LastName='.$LastName.'&Email='.$Email.'&PayFrequency='.$PayFrequency.'&Phone='.$Phone.'&donationAmount='.$donation-amount.'&MailingStreet='.$MailingStreet.'&MailingCity='.$MailingCity.'&MailingState='.$MailingState.'&MailingPostalCode='.$MailingPostalCode.'" width="1" height="1"></iframe>';
?>
The matching field names are correct, as I named the external field names after the field names in the original form. (The one different one, donationAmount, I changed because I discovered PHP wouldn't read it correctly with the dash).