Interesting hypotheses! I can't believe how much you've noticed. You make me want to rewatch ... well, all the Moffat era, actually. :) Anyway, the first one seems the most obvious, and the only one I thought of, but I'm particularly enamoured with the "egg of Gallifray" idea. Very cool.

Oh and if River saves the day I will be beyond thrilled! One of the many possible hints I hadn't picked up on.