I am NOT talking about the mechanics of the trade itself, I am talking about its outcome as far as the probability of the system is concerned.
You are, after all, paying double the spread to initiate two positions.
It's EURNZD. Short.
EURJPY LONG and NZDJPY LONG would not reduce to the natural. It would be two distinct positions funded in yen. Then you could pull-out your ridiculous correlation fiction. I cannot believe that you don't know the most basic FX math.