How do I obtain the result summary from within a form on the view page?
However, the result summary for the view would appear to need to go in
  the middle of the form.
  
  Since this is on a View page, is there a way to get the current View
  and fetch its result summary within a hook_form_alter()?


Don't complicate your Drupal life, and just KISS.

I assume you already added the Result Summary to your View's header. So just:

style.css

.view-id-[your-id] .view-header {

  position: absolute;
  top: 70px;

}