Well, I spent the day carefully recreating the table in segments, and everything was working well until the very end (again). As I got around to the final tweaks, the tables started shifting again

I tried then splitting the table again and then rejoining it but that didn't work either (the rows shift once I combine the table segments.)

Also, I realized that the shifting that is visible on the Outline view is due to the cell left margins (when the text is included, it is noticable that the rows shift so that the text in the first cells all lines up.). So I am assuming that what was seen on the Outline viw wasn't a symptom or cause to the issue.

I'm giving up on this issue for today, I'll reattack it on Monday (assuming I haven't quit or jumped in front of a bus by then)