How to limit the number of results for all query_posts on mysite

It is not that hard to enforce a hard limit on results:

add_action(
  'post_limits',
  function($limit) {
    $limits = explode(',',$limit);
    if (isset($limits[1]) && 2000 < $limits['1']) {
      $limits[1] = 2000;
    }
    $limit = implode(',',$limits);
    return $limit;
  }
);

I would not be surprised if that does not solve your problem though. Just searching over that many posts may be too much for your server, no matter what the limit is on the returned results.

I am also not 100% sure that that will not break things. Be careful.

You could use 'no_found_rows'=>true for any queries that do not need pagination. That might help.

Ultimately, I suspect that you are just doing too much for your server and/or you need someone who is very, very good with server configuration to help you tweak settings and possibly load balance.