Replace/Mute/Stop Search Query

I had a quick grep for SQL_CALC_FOUND_ROWS and found a few instances. I’m not sure which one is being called in your case, but here’s an interesting one from wp-includes/class-wp-query.php line 2904 onwards:

$found_rows="";
if ( ! $q['no_found_rows'] && ! empty( $limits ) ) {
  $found_rows="SQL_CALC_FOUND_ROWS";
}

$old_request   = "SELECT $found_rows $distinct $fields FROM {$wpdb->posts} $join WHERE 1=1 $where $groupby $orderby $limits";
$this->request = $old_request;

if ( ! $q['suppress_filters'] ) {
  /**
   * Filters the completed SQL query before sending.
   *
   * @since 2.0.0
   *
   * @param string   $request The complete SQL query.
   * @param WP_Query $this    The WP_Query instance (passed by reference).
   */
  $this->request = apply_filters_ref_array( 'posts_request', array( $this->request, &$this ) );
}

The important part is that there’s a filter here where you get the SQL and you can do your own checks on it. It doesn’t look like you can stop the query running, but at least you could change the SQL to something that doesn’t bother you 😉

I don’t know what the suppress_filters flag is here, so you’ll need to make sure that that isn’t set.