Create a regular XML post export

Create a new “feed”.

A feed, in WordPress, is basically just a special template with the proper hook. This would do the trick:

function feed_fake($comment) {
...do stuff...
}
function add_my_feed() {
add_feed('fake', 'feed_fake');
}
add_action('init','add_my_feed');

The resulting URL will be along these lines:
http://example.com/blog/feed/fake/ or
http://example.com/blog/?feed=fake
…depending on your permalinks, of course.

Now, the code in feed_fake would be basically similar to the stuff in feed_rss2.php or what have you. It’s just going to output XML, do the Loop, whatever you need to create your XML output. The existing feeds work exactly this way. In their feed functions, they simply do a load_template( ABSPATH . WPINC . '/feed-rss2.php' ); to create their output.

Something along the lines of this would work for the “do stuff”:
load_template( TEMPLATEPATH . '/feed-fake.php' );

The idea is that when somebody asks for the feed, that function gets called. It can do anything you like to generate the feed. If you are putting the feed into a new file in the theme, than that line above will load and run it as any other template.