Screenscrape it with PHP.
PHP Code:
<html>
<head>
<title>Your Youtube Videos ScreenScraper</title>
</head>
<body>
<?php
$page = file_get_contents("http://www.youtube.com/user/InternationalCaller#p/u");
//Your YouTube user name would go there instead of mine!//
//Above this line, ALL WORKS FINE! ////////////////////////////////////////////////////
// FOR you the $getpage should be the entire html you display on the page
$explodefirst = explode('<div class="scrollbox-body">',$page);
$headerisgone = $explodefirst[1];
$explodesecond = explode('<div class="scrollbox-separator">',$headerisgone);
$endresult = $explodesecond[0];
//You can use str_replace to change style elements, link base urls, etc.
/*
$endresult = str_replace('bgcolor="#2b4c3f"','', $endresult);
$endresult = str_replace('width="325"','width="345"', $endresult);
*/
$endresult = str_replace('href="/','target="_blank" rel="nofollow" href="http://www.youtube.com/', $endresult); //setting links to open in new window, nofollow and base YouTube.
print '<div class="scrollbox-body">'; //putting back the DIV we removed in the first function
print $endresult;
print '<p> </p>';
?>
</body>
</html>
I tested it and it works. 
You can get the general idea and tinker with it to show your latest vids.
You can copy the elements you need from the Youtube stylesheet, and use my str_replace to reset the correct URLs, etc.
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