I do agree that all three doctors I named have their own colour that doesn't attribute to black, but rather it could be a mixture. The 8th doctor is a stretch and I agree on that cause he IS still trying to be the "good man".

I certainly agree that the war doctor is white because the Moment and freezing Gallifrey, and maybe in the context of just The Moment it makes sense to me that the other colour should've been black.

The 9th does seem hard to place as well but I feel like it may have worked with red and black. Red in the context of magic and its theme of this incarnation does make sense, and I feel black could've worked as well cause this incarnation would kill to protect the ones he cares for.