This is something I've thought about on the PS4. The cable that goes into the controller has an extra connection for the microphone, which was concerning, but since your HD-600's work then we don't have to worry about that causing problems.
Those little controller jacks are tiny, and they may not actually use a switch to determine whether headphones are inserted, but rather it may be looking for the load of the headphones themselves. What I would do is to go buy yourself a pair of 220 Ohm 1/4W or 1/8W resistors and temporarily install each from hot to ground on the RCA jacks. That will present a convincing load to the controller, and it may get you up and running.
If that does work, I would consider installing those resistors in the RCA plugs on that cable, just so the Crack can be used normally otherwise.
-PB