That seems to be VERY close to _exactly_ what I'm looking for, but it's not quite right (which makes it very far from useful, unfortunately).
The problem is that pressing Ctrl+F4 twice in a row keeps iterating over the 1st, 2nd, 3rd, etc. windows. So if you want to switch between two most recently windows, you have to press Ctrl+F4, then Ctrl+Shift+F4, then Ctrl+F4, then Ctrl+Shift+F4, etc.
The problem is that pressing Ctrl+F4 twice in a row keeps iterating over the 1st, 2nd, 3rd, etc. windows. So if you want to switch between two most recently windows, you have to press Ctrl+F4, then Ctrl+Shift+F4, then Ctrl+F4, then Ctrl+Shift+F4, etc.