Update:
Of course, after writing all that down, I found a somewhat cheaty solution: instead of using <?php include I now use the <object> tag, and low and behold, it works just like it should. The only thing I need to figure out is the target tag, how to get the search results out of the <object> and back into the main window.
Still, it would be interesting to learn why it wouldn’t work via <?php include.
