UPDATE:
I found that, for me, I can recreate the problem by simply splitting a video/audio track and leaving it otherwise intact. That is, I split it, but I do not move it. I leave it in place. (I would normally do something with it after splitting it, for example, swap in a different audio track, but to recreate the problem, splitting the track was enough.)
@[deleted] tried helping me (many thanks) with these suggestions: (1) Make sure my DirectX and graphics drivers were up to date. I did that. (2)Try the latest version of VideoPad. I did that. Unfortunately, these changes did not fix my problem and, also unfortunately, @[deleted] was not able to recreate the problem on his end. That's that bad news.
The good news is I found a clumsy but usable workaround. I found that if I export the video in 2160p (4k) format, the exported video plays without any of the problems that I have been seeing. Then I re-import that exported 2160p video back into VideoPad. And then ... I can export it in 1080p format and everything works.