For anyone that's interested, I found and fixed the problem. It was related
to a table in the header. Actually, there was a header on a cover sheet
(that exists in its own section), then an inner "title page" that had no
header (also in its own section). The title page is followed by the bulk of
the document, which contains multiple sections, but starting at this point
had all of the headers linked ("use same as previous").

The main section had the same header as the front cover sheet (with embedded
table).

I'm not sure why this made Word go "bonkers". But I saw where KB292161
talked about repagination problems in files with tables in the headers. (But
I didn't have a nested table, and change tracking was not on, etc., etc.)

Oh well... didn't want to do it but put the header on the title page and
linked the headers throughout the entire document. This solved the problem
with Word 2003. I haven't tried a machine with Word 2002 yet, but assume the
problem will be solved there too.