MacBook Pro with Touch Bar; switch between F keys, app controls and control strip?
It turns out that I wasn't clear on the four default modes for the Touch Bar:


"App Controls with Control Strip"
"Expanded Control Strip"
"App Controls"
"F1, F2, etc. Keys"


I wasn't clear (actually I think Apple wasn't clear) what the difference was between "app controls" and "control strip". Turns out, if I choose option 1, then I get a (somewhat narrowed) application-specific control bar, plus a (compacted) set of media control keys. So, that gives me access to my first and third desired modes. Then, set "Press Fn key to" to  "Show F1, F2, etc. Keys" and I'm golden.