It's an interesting approach, and while I would not actually remove the default alignment system from my games (never had problems with it), it would be interesting to see where known creature types fit it.
Archons: Pure White, maybe traces of blue and/or green. Militaristic, believe in the strength of society to benefit the individual.
Modrons: White/Blue, clearly. Laws are the defining aspect of the multiverse, and they are also big on discovery and research.
Baatezu: difficult. Clearly white for order, probably also black. Yes, Black/White sounds right.
Yugoloth: the definition of Blue/Black. A society of power and secrets, full of constant backstabbing and treachery.
Tanar'ri: easily Red/Black. A rare few Tanar'ri might have traces of green and blue in them, but those are rare cases.
Slaad: Red, with Black or Green depending on the individual.
Eladrin: Green, with Red and White mixed in.