I'm cautiously optimistic: After doing more research and playing around, trying fixes to similar issues others have posted on the web, I've been able to make some progress on resolving the problem.

In the Word document, type Alt-F9. Every link or merge field or anything similar that you've included in the document will appear. Go find your chart links, and edit the source there.

The change will stick as long as you have it open (including after saving the document), but will revert back upon closing and re-opening. I'm trying different things, like locking the links before closing, telling Word in the Web Options section not to update links upon saving, but nothing I've tried seems to work. I can (and did) create a macro to correct the links, but there's been problems opening the document in one office location if the links were created on the server of the other office location, so I'm worried that the "just press a button to run a macro after you've opened the document" strategy won't work.

Any thoughts on getting the change to stick upon closing and re-opening?