Okay -- made the following changes:
<input type="hidden" value="<?php echo((isset($_GET["Player"]))?$_GET["Player"]:"") ?>" name="PlayID"> (hidden element)
<form class="secCopy" id="TrainSelect" name="TrainSelect" style="margin:10px 100px;" method="post"> (2nd form)
<input type="submit" name="ATC_Submit" id="Submit" value="Submit" formmethod="post"> (Submit Button)
Now the page reloads with just the filename in the address bar -- no other arguments. . .
Thanks. . .