Projector black at any resolution when connecting MacBook Pro Retina
Opposite of your thoughts that the problem lies at the Mac end, I'd personally search on the projector first.  If the supplied signal is somehow out of range, the projector should beam some feedback by showing an error on the wall.

Perhaps you haven't selected the right source on the projector.  Does the projector handles a different HDMI source correctly?

Being such an expensive projector and all, connecting it to a (n old) Apple TV could do wonders.  It's cheap, neat, wireless and well implemented in OSX and iOS.  If your environment is Apple focused I won't hesitate and try it out.