I just wanted to briefly explain how I finally got these forms to work using the REST API, in case it can assist someone else.
At first I had these forms embedded inside an iFrame, but then found out that the auto-generated email from the REST API code (by using the "Save my progress" feature) could not link directly back to an iFrame page.
So, after converting the iFrame to an "overflow div" and with the helpful assistance of dbuschho, I have come up with the coding to make this work.
HEAD SECTION
<style type="text/css"> .divScroll { position:relative; /* this line is required to fix the IE6 and IE7 overflow related issues, it does not affect other browsers */ height:400px; width:700px; overflow:scroll; } </style>
BODY SECTION
<div class="divScroll"> <?php if(!isset($_GET['tfa_next'])) { echo file_get_contents('http://app.formassembly.com/rest/forms/view/YOUR_FORM_NUMBER'); /* make sure you use a single quotation here and not a double */ } else { echo file_get_contents('http://app.formassembly.com/rest'.$_GET['tfa_next']); } ?>
Hopefully, this will help other people who might want to achieve a similar layout but without the several hours of work it took to figure this out.