The fix: Tools > Customize Keyboard... > Window and Help
The kind folks at the MS Word forums had the answer!
You have to set the shortcut manually by going to:
1) Tools > Customize Keyboard....
2) Under categories, click on "Window and Help"
3) Under commands, click on "NextWindow"
4) Click in the "Press New Keyboard Shortcut" box and type Command-tilde
Repeat for "PreviousWindow", choosing Command-shift-tilde