I only know very little from reading Dr. Wilson's site.
The short of it is that you need bio-available copper for your hair color. Copper detox will likely be pulling out all copper from your body, not just the unavailable oxidized form.
So maybe you could either take breaks, reduce the amount of zinc or add in more bio-available copper to your diet.
Usually people who are copper toxic have very bad reactions to high copper foods like nuts, beans or chocolate.