Have a pic of this chick?
Paint is just one copy of dominate white on black.
Usually one copy of dominate white will cover almost the whole bird with only specks or splotches showing.
Paint breeders have been breeding towards more black showing since the paints have been around.
Your reverse paint will still be the same genetically so just continue to breed it as a paint and only use the offspring with the most black to move forward with your project.
Since paints only have one gene for dominate white they don't breed true.
You have a few options.
Breed it to a black and get about 50% of the offspring being paints. The rest being black.
Breed it to a white and you'll still get about 50% paint offspring but the others will be white.
You can breed a pure white from that cross back to black for 100% paints. The pure white ones will have two dominate white genes so all offspring will get the one gene they need.
You can breed that paint to another paint and get 50% paint, 25% black and 25% white.
If it was me and these are just my thoughts.
There is something different about this chick that is letting way too much black leak through so I would want as many of its genes to move forward and I wouldn't want to bring in any other dominate white.
That way I know its white is all I'm working with.
Breed it to a black. Breed those offspring that are paints back to this chick and/or to each other.
After that pick the ones with the most black and continue breeding them to each other.
After a couple generations you can pick some of the pure white offspring and breed them to some new blacks to bring in new blood.
Just don't bring in new dominate white and don't breed any paints or blacks that show any other color leakage.
Again that's just my theory.