The work-around does not solve the initial symptom of the overlay that would not reappear. It just avoids the immediate need for it. I contacted Goodiware for advice here. The developer told me to try a single tap right in the center of the screen. This seemed a bit counter-intuitive, as the overlay appears along the edges, which is where I had been concentrating my tapping. Regardless, I tried it; it worked. The overlay returned.

This was good. However, there is still an aspect of the symptom that remains unresolved. The area of the screen where a single tap will bring back the overlay is much greater for some documents than others. In my testing, it was only with PDFs that I had to restrict myself to a small spot in the center. For other types of documents, I could tap almost anywhere. This is why I initially thought there was no solution for PDFs.

What if GoodReader (or a similar app) had failed to provide a backdoor "emergency recovery" setting? And what if even tapping at the center of the screen had not worked to bring back the overlay? What then? How would you ever break out of the circular loop (of the document automatically opening on every launch) so as to regain use of the app?