Wuth the JVC 1D LUT, remember that black and white are locked in the LUT application.
That means all the LUT can do is correct relative grey scale issues between black/white.
So you really need to target the actual white of the projector, rather than the final colour space white point!
As it is a 1D LUT I would just use a large Grey Scale Only quick profile, not a cube profile.
Either the one within the quick profile options, or make a CSV file to your own specifications.
(Augment may help too...)
And no, picture data/colour profiles are not supported, as I can't see any benefit from doing so (if possible at all).
Mob Boss at Light Illusion