Not breed on white because white hide all color-genes so it's a complete unknown factor.
When you breed on Quail you know what you are dealing with.
Quail should have as genotype eb/eb Co/Co Ml/Ml (based on Silver or gold this you not mentioned)
Black should have as genotype E/E (when you not find a single Silver or gold feather in the neck you can't tell if it is based on Silver or gold) (when you can see much green shine you can consider it have the black-pigment intensifier gene Melanotic in double (Ml/Ml) or in single (Ml/ml+) doses).
The result of this cross would be unpure black phenotypes E/eb Co/co+ Ml/Ml or Ml/ml+ (based on Silver or gold but not so important when the goal is pure Blacks)
When you now cross back on the Black father or you cross the F1 x F1 you will become a percentage pure Black (E/E) offspring, which your problem is solved in 2 generations.