Oh, that changes things :)
To use the existing connection, you need to use php's mysql_* functions, which is very roughly the same as using the $wpdb object. As long as you are careful, it will work. To use WP functions, you need to load the WP environment, which will open it's own connection. You normally do this by including wp-load.php on your page. I haven't tried doing this outside of the WP directories, but it shouldn't make any difference.
DB work outside of WP is not part of my experience, but the wp-load include probably needs to be inside a function to ensure it is not run before the other connection is closed. If it were me, I would go ahead and use the existing connection. I would analyze the insert statement sent from wp_insert_post() to ensure I've got my own statement right. Then test thoroughly that WP sees my insert as a valid draft post before turning my script loose.