Hold on, wait a minute, put a little... nevermind. Not a song to sing at this time.--- You have already stated that you don't like to breed unregistered horses, so how about a deal?
Like someone already said, the mares conformation, breeding soundness, and disease testing would play a big part. Now, lets say she has almost flawless conformation, her breeding soundness(from a vet) comes back perfect, and you get her tested for common diseases in morgans and quarter horses and she gets a clean bill of health.
Then, and only then would I suggest you go on breeding her. Though at that point, you have put in mind a stallion. One with good conformation, breeding lines, and will fit your disipline. What I would suggest here, and this is where the deal comes in, finding a paint stallion that is what you are looking for. If my memory serves me correctly, you can register a horse as a pinto even if only one parent is registered. (Someone correct me on this.)