I discovered after some additional poking around, that it’s possible to turn of the automatic syncing of the last read page (and bookmarks and notes) on shared books. There is an option all the way at the bottom of the Kindle management page that allows you to turn off that feature.
It doesn’t give me all the content control I’d like, but at least the “sort by most recent” lists won’t be affected by the activity on the opposite Kindle.
TECHBUNNY 