Offset is the same as Bias.
But, if you adjust the P7 controls I would indeed expect the RGB Separation to then be bad!
Any display that has control of secondary colours (CMY) immediately says the colour management is bad!
Secondary colours should be a direct calculation of the Primaries, and not require separate control - to do so will cause very bad RGB Separation.
So, overall it looks like the projector's internal colour management is very bad!
I would use Offset and gain only, with everything else turned off.
If you can do that - turn everything off and use a LUT only!!!!
Mob Boss at Light Illusion