Just a shot in the dark, but to prevent the copper etching away on hobby circuit boards, you used to cover the pathways with a permanent marker. It would prevent the acid from etching the copper underneath. You could try making an inverse of the mask you’ve been using (something that would cover area that you are trying to patina) then use a permament marker to color in the inside disk area that you are trying to protect. Remove the mask and put the patina on, then use denatured alcohol to remove the marker. I haven’t tried this myself, but it seems plausible since the marker would prevent the surface from oxidizing in the same way it protected copper from acid etching.
Just a thought.