I often discover that I completed something a few days ago and I would
  like to mark it done with the appropriate date as though I had marked it
  done in the past.  That means, e.g., for a repeating event it might
  repeat sooner than if it had been done today.  Is there a way?

I also want to to that, basically binding 'now' to a particular time in
the past and then executing a todo state change (to effect the log, and
also the next scheduled time).
I wonder if replacing the calls to get now with a function that looks at
a variable and doing

  (setq now-var (now))
  (do-whatever)

would be enough to get it to do what I want.