I'm going on the Missy = The Master theory too. And if she isn't the Master I think it's still high odds that she's a Time Lord.

(I'm just really hoping that Moffat doesn't do some kind of convoluted thing where River becomes the Master because... no)

I like your theory about her materializing a TARDIS around the Doctor's collateral damage at the last possible moment. I don't think it's crack at all. In fact, I think it's the most plausible theory I've heard so far.