Custom Formatter: Rendering an image preview of a PDF (Private File System)

I have created a custom formatter that reads an attached PDF file, and creates a redered JPG file for display as a preview (Custom formatters ROCK btw) — ( code inspired and ported over from: http://drupal.org/project/pdfpreview ). My only issue is that my site is using "Private Downloads", so the rendered JPG, which is saved in the "private" directory, is not viewable, even to authenticated users.

Anyone have any ideas as to how I can allow users to view the rendered jpg files, without saving them *outside* of the private files dir?

Setup:
- I have a node with a PDF file attached
- The whole site is setup for "Private Downloads"
- I have a Custom Formatter, that creates, and saves a JPG preview of a PDF when the node is displayed
- The JPG preview is saved in the /sites/default/files/private/pdf_preview directory

Problem:
- I am trying to display the created JPG preview file, but even authenticated site visitors can't "see" the image file, because it's in the "private" directory.

Here is the code I'm using in the Custom formatter (you need ImageMagick install on your box for this to work):

if ($variables['#object']->field_asset['und'][0]['filemime'] == 'application/pdf') {
	/* Yes we're dealing with a PDF */
	/* Set and create preview storage directory, if not already exsisting */
	$output_uri = file_default_scheme() . '://pdf_previews';
	$output_dir = drupal_realpath($output_uri);
	
	if (!file_exists($output_dir)) {
		$create_dir = drupal_mkdir($output_dir);
		if (!$create_dir) {
			/* TODO Add error handling if directory can't be created */
			} 	  	
		}  

	/* Set preview filename	*/
	$fid = $variables['#object']->field_asset['und'][0]['fid'];
	$output_filename = $output_dir . '/' . md5('pdf_preview' . $fid) . '.jpg';
	
	/* If this preview does NOT exsist, create one */
	$pdf_uri = drupal_realpath($variables['#object']->field_asset['und'][0]['uri']);
	if (!file_exists($output_filename)) {
		$command = "'" . $pdf_uri . "' -colorspace RGB -geometry 500 -quality '85' '" . $output_filename . "'";
		_imagemagick_convert_exec($command, $output, $error);
	}
	
	$rendered_uri = file_default_scheme() . '://pdf_previews/' . md5('pdf_preview' . $fid) . '.jpg'; 
	$rendered_url = file_create_url($rendered_uri);
	$rendered_image = '<img src="' . $rendered_url . '">';
		
	return $rendered_image;
	
} else {
	print "This is not a PDF";
}