Congratulations! You are, at this very moment, shorting your NW-ZX300's AMP! Good luck going back to Sony once your unit is done working, I am fairly sure this kind of damage is not covered by warranty. Also if you can't notice the huge hiss/ hum you get plugging in those headphones on a balanced connection, you must have serious hearing problems.
The wirings of the internal connector on the MDR-1000X or WH-1000X series are NOT meant to be connected to a balanced output (as in, ever, it's just not engineered that way) because the ground is shared between both channels in the connector itself, all you will do wiring those this way is 1. Damage your source's AMP 2. Create heavy distortions in the sound you are hearing, nothing you do, can do, will do, will change that fact, unless you are willing to literally open these headphones and rewire them internally that is (good luck with that, I hope you have some serious soldering skills).
Sometimes the kind of things I read on this forum wants to make me pull my hairs out.
Wow, I will post here if I hear the broken AMP noises. I just start using it for only 120HRs.
And I have no hearing problems. Thanks for your advice.
For now don't do this at home.