Was the test pattern extremely digitized?
Did you try and twist the projector to see if the pattern remained the same? If this is moire, the pattern should not remain the same. If it's coming from the projector, I'd expect the pattern to remain constant.
Example: If you turn the projector 45 degrees and this pattern also moves 45 degrees VS you turn the projector 45 degress and the shapes and lines change drastically.
I know this is a hassle.