Since the search input/controls cannot be moved, and they are absolutely positioned, it's possible that they hide content in the top-right corner.
One Idea I had for this was to add opacity to the background and slide it off the right side of the window until just the controls are showing. Then, add a button, or maybe just click on the selected/total found counter, or maybe show a bit of the search field to be clicked on to bring it to the foreground again.