If you have trouble with washed out blacks on the Sony Full HD Projectors, try these settings:
Go to the developpers options in Zappiti settings, then select RGB 4:4:4 instead of "auto" in space color.
Dynamic Range on the projector : Limited
Zappiti : HDMI Range Full
These settings are only good for 1080p projectors because it allows only 8 bits in this mode.