How do I get thumbnail generator to recognize the_permalink tag?

the_permalink() is actually filtered in the Recommended Links plugin to echo a custom meta field called _href. If you want access to that field without echoing it, you can use get_post_meta( $post->ID, '_href', true ).

Try something like this in your loop:

global $post; // may or may not be necessary
$url = get_post_meta( $post->ID, '_href', true );
$width = 300;
echo bm_mshot ($url, $width);