A family of Microsoft word processing software products for creating web, email, and print documents.
I clearly don't know as much about this topic as I'd need in order to help you. It just occurred to me that CSE style, and the other citation order styles, aren't present in Word as shipped by Microsoft. Are you using styles from BibWord or some other source?
When I use the CSE - Citation Sequence style from BibWord, it does order the bibliography in citation order, but it also includes the citation numbers:
> If I had to go look at where Word is told how to order, that would be in the style xml file itself, right?
> Could you point me towards where that is? And what the command is?
Assuming you are using the BibWord style file, it should be in %appdata%\Microsoft\Bibliography\Style\CSECitSeq.xsl.
Open that file in a text editor such as Notepad. Search for the string b:SortKey. That element appears to control the sort order, but I haven't figured out how.
If you need better advice, contact the author of the style file, Yves Dhondt. His email address is in the comment block at the top of the file. Yves used to contribute here, but I haven't seen him post for a while.