Time for AJAX
One way to reload the page but not the map settings is to use AJAX, or Asynchronous Javascript. This lets the submit button call the server, and the server responds with the answer, the section of the page gets updated (via the HTML document object model e.g. var newSection = getElementById('thisTag')
It works beautifully. I did mine "by hand" but there are many frameworks and helpers out there for non programmers. This example you cited is the perfect application for AJAX because you don't want to reload the entire page if it has a map on it.
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