OK, well this did not get resolved by doing any of the above.
Here is what I discovered to solve the problem. I did not discover why it happened, but it appeared that Microsoft Word got very enthusiastic in adding font attributes to my fifth level heading style.
Until now I have not had access to corrupt document so I have not been able to test my hypothesis regarding why it happens.
There are a few actions that one starting to adventure with creating styles and templates without first having studied and understood the proper methodology to create hierarchic numbering in a document is intuitively led to do.
Applying one of the lists from the multilevel list library then, try to modify it by doing "modify" on one of the headings/title (choosing format, numbering). That modifies the document active list but not the library list and if not done from a top level
heading, can create a conflict within the same list for that document.
Trying to modify a list style by applying a library list over it (it saves it as a new style automatically but does not attach the headings/titles properly) and if it is not added to the library, when opening the document word seems unable to apply the alterations
that were made to the library list when it was reapplied to the document
Getting confused as to where change what. If trying to change the actual list, doing it through the adjust indents (which is the correct way for a list style but not for a library list because of the reason above) and saving it as a list style. In which case
only that heading paragraph is now attached to this list style while the rest of the document hierarchy is governed by the library list or the previous list style.
If indentation has been set both in the style definition of the heading/title and the list style, they will conflict and then it is likely for a beginner to modify the indents in the library list or style list or even from the menu adjust indents and not notice
they are creating an additional list rather than fixing the original one.
The solution for someone who does not want to go into the xml stuff, for a big document, is to create properly (not setting indents nor numbering, cascading H1 based on no style, or normal and H2 on H1 CREATING them in the right order H1, H2, H3,etc) a new
title1correct, title2correct, and so on, to search and replace styles (title1 by title1correct). Then to create a new list style to define indents and numbering and attach the titlecorrect styles to the appropriate levels.
Usually that's sufficient for fixing it but if not, 2 more strategies can work:
Putting the cursor on the first occurrence of H1 and applying the list style but making sure its the right name one)
Doing search for all H1, clicking on "erase all" and right after, while the text is still highlighted, apply style H1. It remove unnecessary code. Do the same thing for the lower levels H. Since they are attached to the list style, they will automatically reset
to the proper numbering.