Alter query (programmatically) after the query is built without using hook_views_pre_execute

To overcome the lack of UNION support in Views, I use the trick suggested by merlinofchaos in #1013774: Is there ANY way to combine results? (Pls view attachment) - "use hook_views_pre_render(), execute an alternative display (recommend an attachment that is not actually attached to anything), then merge $view->result."

I have several page displays that could use almost the same attachment, so I was hoping I could do something like:

    $other_view = views_get_view('my_view', TRUE);
    $other_view->set_display('attachment_1');
    $other_view->build();
    // Modify WHERE clause depending on which page display is used:
    if ($view->current_display == '...') {
      $other_view->query->where [....]
    }
    else {
      $other_view->query->where [....]
    }
    $other_view->execute();
    $view->result = array_merge($view->result, $other_view->result);

but it doesn't work. Neither does $other_view->query->add_where ... The executed query is still unaltered.

Apparently, the query is built and stored somewhere else - in the SelectQuery object in $other_view->build_info['query'] maybe - and $other_view->query is just kept for reference (and not used when executing the view). Am I right? If I'm right, this could be made clearer in the documentation of the build function.

And finally - the real question: Is there a workaround for my use case? (I don't see how I can use hook_views_pre_execute since the modifications depends on my page displays and not something in the attachment itself.)