The exact genetic composition of paints is unknown; they do carry dominant white, but at least one source I read said that they are not related to exchequer legnorns. However, since the original paints came about from a cross to a leghorn, I am not sure how much weight to give that statement. I do not think one could re-create them without knowing their genetic composition; however, my best guess is to cross to an exchequer leghorn and in about 10 years you may have something similar (that is about how long they are already into development).
edited to add: If at some point I decide to get paints, I would not try to recreate them. DItto for showgirls or any other breed or variety that is already many generations into development.