I am leaning towards doing it in the Emacs side since it would get rid
of similar annoyance(s) in other yank-media handlers, not just Org.

If no one beats me to it before the end of this week, I will propose a
patch to take care of (1).  It would be preferable pinmacs if can take
care of (2) if we decide to take care of it from the Emacs side since I
will probably not be able to describe the situation well.