It seems like there must be a way to search for (and hopefully perform group operations on)contacts that are in both Group A AND Group B but I can't find it. Suggestions?
You can use Search Builder (Search > Search Builder) to search for contacts in a group A and add another search field for contacts in Group B. See screenshot from demo.
Under Search > Custom Search there is a search called Include / Exclude Search which is specifically for this purpose ie including/excluding specific Tags and Groups. You can see it here on the demo site.
I don't know if it delivers what you need but worth knowing about.