Curious that my original recipe (fixing the C-x C-x to C-x C-c, as I
suppose I intended) doesn't work now because

  emacs -Q -f desktop-read

does not read the desktop file from the current directory ('.' is no longer
in desktop-path).

But anyway, back to the issue:

> Hm, I think I was wrong here -- I'm not getting exactly the same errors
> as in earlier versions of Emacs, but the data that's saved still isn't
> usable.

Correct.

But, I suppose it is perhaps not worth fixing now, because after that we
implemented framesets, and you can do

C-x r f a

and the frameset in register a is saved and correctly reloaded afterwards.
It's a bit of an overkill, of course.

If we want to fix it, perhaps we could trick our way, by using framesets to
save a one-frame frameset with some special info to mark that it is really
intended to be just a window-configuration, and then, when reloading the
desktop, restoring somehow the window configuration into the register, from
the frameset data. No idea if it is worth the effort, but I think it would
be doable.