I went back for another go at this. I opened the troublesome document, and verified that the same page jumping was still occurring. I then verified that the front matter, 14 pages in this case, was all in one section. The following 25 sections were each in their own section. I do that for two reasons: I want to be able to add or subtract material in any chapter (section) without displacing all of the following text in subsequent chapters, and I want each chapter to start without a page number on the first page. That is standard practice. I still end up with an occasional number on a trailing even page that is blank, and I remove that lonely page number in Acrobat. The goal here is—no page number on the first page of a chapter, and no page number on a completely blank page.
Then I ran page numbers consecutively from the first page of the front matter through the entire document. That worked, and it stopped the page jumping, as I had experienced before. I still wanted to start the first chapter on page number one. This time, I put the cursor in the first page of the first chapter, and went to insert page number, and clicked on format, and clicked on start page at, and typed in 1, and left page number on first page blank. This time it worked! I did not change any section breaks at all. They remained the same as they had always been. And the pages no longer jump around, and the page numbering is just as I want it. I printed the document to Adobe PDF, and this time there were no strange blank pages showing up at all. The only thing left to do is to remove the page numbers in the front matter. I tried all of this with front matter pages formatted as Roman numerals, and that gave me the same problems as before, though it should be possible to do that. I actually prefer not to have any page numbers in the front matter, so I just remove them in Acrobat.
Another strange thing I discovered; this particular document has two pages of endnotes—the last two pages in the document. The last page is an odd number page, on the left side. I have to end the document with an even number of pages, as the printer requires that. I tried to insert a blank page after the page with the endnotes. That cannot be done. The program has, in some way, reserved that page for endnotes, and there was no way I could put in a blank page at the end. But I can easily put in a blank page at the end in Acrobat. There is no option in Acrobat to insert a blank page, as there is to delete a page. But I always have a single blank page PDF, made from a single blank page in Word. It is necessary, when doing that, to first format the blank page, even though nothing at all is on it. I format my pages to 6x9 inches. Otherwise you get a page in Acrobat that does not fit into the other pages.
So, this problem has been solved for me. I still think that there is something buggy in Word's page numbering machine. I tried many ways of linking and unlinking headers and footers, and different ways of inserting page numbers. That it suddenly worked so well was a pleasant surprise.