Meta query terribly slow

I’ve come across this problem and it seems MySQL doesn’t deal well with the multiple joins to the same table (wp_postmeta) and OR-ed WHERE that WP generates here. I dealt with it by rewriting the join and where as mentioned in the post you link to – here’s a version that should work in your case (updated for WP 4.1.1) (updated for WP 4.2.4):

function wpse158898_posts_clauses( $pieces, $query ) {
    global $wpdb;
    $relation = isset( $query->meta_query->relation ) ? $query->meta_query->relation : 'AND';
    if ( $relation != 'OR' ) return $pieces; // Only makes sense if OR.
    $prepare_args = array();
    $key_value_compares = array();
    foreach ( $query->meta_query->queries as $key => $meta_query ) {
        if ( ! is_array( $meta_query ) ) continue;
        // Doesn't work for IN, NOT IN, BETWEEN, NOT BETWEEN, NOT EXISTS.
        if ( $meta_query['compare'] === 'EXISTS' ) {
            $key_value_compares[] = '(pm.meta_key = %s)';
            $prepare_args[] = $meta_query['key'];
        } else {
            if ( ! isset( $meta_query['value'] ) || is_array( $meta_query['value'] ) ) return $pieces; // Bail if no value or is array.
            $key_value_compares[] = '(pm.meta_key = %s AND pm.meta_value ' . $meta_query['compare'] . ' %s)';
            $prepare_args[] = $meta_query['key'];
            $prepare_args[] = $meta_query['value'];
        }
    }
    $sql=" JOIN " . $wpdb->postmeta . ' pm on pm.post_id = ' . $wpdb->posts . '.ID'
        . ' AND (' . implode( ' ' . $relation . ' ', $key_value_compares ) . ')';
    array_unshift( $prepare_args, $sql );
    $pieces['join'] = call_user_func_array( array( $wpdb, 'prepare' ), $prepare_args );
    // Zap postmeta clauses.
    $wheres = explode( "\n", $pieces[ 'where' ] );
    foreach ( $wheres as &$where ) {
        $where = preg_replace( array(
            '/ +\( +' . $wpdb->postmeta . '\.meta_key .+\) *$/',
            '/ +\( +mt[0-9]+\.meta_key .+\) *$/',
            '/ +mt[0-9]+.meta_key = \'[^\']*\"https://wordpress.stackexchange.com/",
        ), '(1=1)', $where );
    }
    $pieces[ 'where' ] = implode( '', $wheres );
    $pieces['orderby'] = str_replace( $wpdb->postmeta, 'pm', $pieces['orderby'] ); // Sorting won't really work but at least make it not crap out.
    return $pieces;
}

and then around your query:

  add_filter( 'posts_clauses', 'wpse158898_posts_clauses', 10, 2 );
  $posts = new WP_Query($args);
  remove_filter( 'posts_clauses', 'wpse158898_posts_clauses', 10 );

Addendum:

The fix for this, ticket 24093, didn’t make it into 4.0 (plus it didn’t fix this issue anyway), so originally I attempted a generalized version of the above but it is too flakey really to attempt such a solution so I’ve removed it…