OK so found the solution to this.
In fact by the time Frontend Uploader has finished its work and returned to the page, the $_POST variable has been stripped. The way to do it is to include the following in the functions.php of the theme:
add_action( 'fu_after_upload', 'my_fu_after_upload', 10, 3 );
function my_fu_after_upload( $attachment_ids, $success, $post_id ) {
// do something with $_POST['destinationField'];
// at this level, $_POST still has data in it
}
