add_filter to the_content after apply_filters

if you want to keep the current setup, try to hook in early and use do_shortcode():

function av_standalone_doc_404($content) 
{
    remove_filter( current_filter(), __FUNCTION__ );

    if ( has_term( 'standalone-document', 'formats' ) )
    {
        $filtered_content = do_shortcode( $content );
        // …

If you want to avoid repeating shortcode outputs use a static variable in the shortcode handler:

function shortode_handler()
{
    static $done = FALSE;

    if ( $done )
        return;

    $done = TRUE;

    // create the shortcode output; this will happen only once.

    return $output;
}