Summary
Same changes as before, but now I'm adding an onbeforeunload event that clears the click event before jQuery's unload event is triggered. This significantly speeds up the transition away from this page.
Script
Select "File_1", then after it loads, select "File_2". Good. Now, select "Select File". No problems. Now lets try clicking "jQuery Profiling" to return to the main page...hopefully we've sped things up.