Strikes me whoever was in charge right now would be struggling. As I say I'm not trying to excuse Moffat from his part in all this, but he isn't the all powerful anti-Christ some seem to think he is.
Seems to me that the BBC needs to hire some help for Moffat. Not a huge increase in the budget, but some people to help keep the production organized and on-track even when Moffat is distracted by, say, Sherlock.
Or, hire more help for Sherlock, so he can focus more on DW.
He can still be the showrunner but things shouldn't come to a standstill when he's overloaded.