Custom SQL query slows down when using multiple OR ... LIKE ... in posts_where filter

I have built a posts query that includes a custom table in search using the posts_join and posts_where filters.

Now the customer wants me to include yet another custom table in the search, but doing so increases query time from an instant to over 5 seconds.

This is what I have done:

function my_posts_join( $join ) {
  global $wpdb;
  $old_table = wp_some_custom_table;
  $new_table = wp_another_custom_table;
  if ( is_search() ) {
      $join .=' LEFT JOIN '.$wpdb-postmeta. ' ON '. $wpdb-posts . '.ID = ' . $wpdb-postmeta . '.post_id ';
      $join .=' LEFT JOIN '.$old_table. '  ON '. $wpdb-posts . '.ID = ' . $old_table . '.post_id ';
      $join .=' LEFT JOIN '.$new_table. '  ON '. $wpdb-posts . '.ID = ' . $new_table . '.post_id ';
  }
  return $join;
}

The additional join doesn't noticeably affect performance, but when I edit the posts_where clause like this...

function my_posts_where( $where ) {
  global $wpdb;
  $old_table = wp_some_custom_table;
  $new_table = wp_another_custom_table;
  if ( is_search() ) {
    $where = preg_replace(
        /\(\s*.$wpdb-posts..post_title\s+LIKE\s*(\'[^\']+\')\s*\)/,
        (.$wpdb-posts..post_title LIKE $1) 
          OR (.$wpdb-postmeta..meta_value LIKE $1) 
          OR (.$old_table..text LIKE $1) 
          OR (.$new_table..text LIKE $1), // -- this kills it
        $where );
  }
  return $where;
}

The additional OR condition slows everything to a crawl.

Any ideas how to speed this up or structure the query differently?

So far I have indexes on post_id in both custom tables. Any other indexes that would help?

Also I have read the advice to break up OR conditions into multiple queries and use UNION on the results, but I have no idea how this would be possible in the context of WordPress filters.