Create your new pages on aspx, and just serve 301 permanent redirects from the HTML pages.
Search spiders are smart enough to realize the content has moved and will not penalize you.
Both Google and Yahoo also say that they parse a meta-refresh with no delay as a 301 redirect, so just do something like this:
<html>
<head>
<title>Moved to new URL: http://example.com/newurl</title>
<meta http-equiv="refresh" content="0; url=http://example.com/newurl" />
<meta name="robots" content="noindex,follow" />
</head>
<body>
<h1>This page has been moved to http://example.com/newurl</h1>
<p>If your browser doesn't redirect you to the new location please <a href="http://example.com/newurl"><b>click here</b></a>, sorry for the hassles!</p>
</body>
</html>