I think . . . . the problem is resolved. Longedge, thanks for suggesting looking at aspect ratio. I believe that was the problem. I am a bit furious that PowerDirector is not smarter than this, or that the instructions don't tell you that consistent aspect ratio is critical.
I used Lightroom to change all jpgs in one section to conform to 1836 x 3264 (16:9) after first doing the same thing at 1920x1080 (16:9). I then made a very short slideshow by dropping them on the timeline and producing to: MPEG-4 1920x1080/30p (16Mbps). It worked perfectly. I then dropped transitions on all, and even added one mp3 file for soundtrack. Perfect!
I think I was doing at least two things wrong over the various trials.
1. too many different aspect ratios in all the various jpgs due to cropping and maybe multiple camera sources
2. sometimes working in 4:3 ratio setting in PD14, yet saving to a non- 4:3 MP4 output file (why does PD allow this???? There are warnings about so many other obscure settings . . .)
3. produced at a non- 16:9 profile (for example, I tried 2048 x 1080 at least once, with the new jpgs sized to 1836 x 3264, and had consistently bad results.
I wish PD would inform us in the Produce mode what the aspect ratio is of each profile that is available. I did not see anything in the manual under slideshow that aspect ratio of images needs to be consistent, or that aspect ratio of images needs to match the produce profile.
Maybe this is obvious to more experienced video editors, but I have done a "lot" of video editing over many years, and truly a staggering amount of still image editing of many kinds over the decades and this was not obvious to me. I did have a nagging question about this in my mind, but the program has so many parameters to consider that it was hard to figure out what could be the problem.
I am very grateful to everyone who suggested things to try. I learned a lot about the program in the process, though I had successfully edited several videos earlier in the year without much trouble, there is still so much to learn.
I will report back after the complete project is (hopefully!!!) finished. I need to completely recreate everything yet again, but now I feel much more optimistic.
I hope this thread helps someone else in the future!!!