Me personally, if I were handling the Bat and intended to have a mass-Arkham break out and AndyC's pre-existing Joker stuff.

...I'd probably just write it that the two events are flip sides of the same coin and that each occurred in the wake of chaos of the other.

i.e.  Guards scrambling to prevent one break, leading into it being easier for the other take place.

But I'm curious to see how [@Roman] would handle it.