How to quickly screenshot all apps in all screens & folders?
This is a bit of a stretch but might work.

I have heard that if you plug your iPhone into your Mac and start Quicktime Player there is an option (possibly under the file menu) to capture what is appearing on the screen of the phone. 

If that does (still?) work then doing that would allow you to go through the whole iPhone's UI as fast as you like recording everything as you go in one Quicktime movie that you can save on your Mac and pause as needed as a reference to how it was set up before.

Note I haven't tried this myself but it sounds like it should work...