This is my method, especially because it shows how design will progress, with tight deadlines this becomes harder but I still consider it a very valuable way of proving work (only a minor designer though with freelancing)

I certainly can understand stand the move fast method of quickly changing things, when I'm doing concept work this makes more sense here.

Long term though, if you actually care about your work you should be making copies or different boards to show how and when you made some decisions. Especially mayor design changes.(Granted I could just be a bad designer that just can't come up with a better workflow)