I have not looked at that script, but you are saying that you can run rss2html.php and get the output that you want, but you want that output inside your own index page instead? You mention that your home page is already named index.php, so it's already a PHP script or at least ready to add script. Just try adding the entire rss2html script in your index.php page where you want the output. This is kind of a messy way to handle it, but will either work or help you start to see how to put it together.
So something like this:
[PHP]
<html>
<body>
This is my index.php page. It's full of lots of great content.
Here is where I want the rss feed to show.
<?php
#INSERT rss2html.php code here
?>
This is the rest of my index.php page.
</body>
</html>
[/PHP]
Let us know how it goes.