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Generally, you need to apply

Generally, you need to apply WB before demosaic (if your demosaic method use something like luminosity maps, the components should be balanced before).
Also, bias subtraction should be done before WB (and demosaic).

I do not think, that max(R,G,B) will give you good BW image. Better use something like RGB to Y[CC] or Lab conversion and use Y or L channel as BW image.

-- Alex Tutubalin @LibRaw LLC