Yes California has the model...they recently raised it to 30k. The regulators there are very hands on (unlike in New York which pretty much leaves the hospital association to regulate itself.)
Another thing NY could do is to amend the tort law to consider lack of staffing not in compliance with state staffing plans as a direct cause for malpractice. Then the state doesn't even have to enfore the law a bunch of ambulence chasing lawyers will do it for them. Most of these hospitals are self insured, let them pay for all the injuries they cause patients who fall on the way to the bathroom because a nurse had 3 tele patients AND 3 med surg patients that day.