So it's a bit complicated to get it to work, not sure if it can even work the way you want to.
I managed to get the contact 7 form to load in the search results, but then it submits to the admin-ajax with the store locator params set, which doesn't work. Is the contact form supposed to use AJAX submit?
You can see the code I used here. Maybe it helps you get started, and find a way to make it work after all. I first collect the output from the do_shortcode under the 'contact_form' key, and then use that key again to access the form in the search results.