In addition to everything else, why not document these things for your local congressman (State, not Federal) & point out how efficient the system is in other states. NY: surrender your plates to the DMV when you sell the car. NY: insurance companies must *immediately* notify the state of any lapses in auto insurance. 1st lapse, you can pay a fine. 2nd lapse, you must turn in the plates for the number of days that you had gone without insurance, else you lose your license. Police cars: can read license plates while driving by & check them against the database automatically. Result: the vast vast majority of people on the road have their cars properly registered & have insurance. Makes it a lot better for the rest of us law abiding citizens to not be in a state where 20% (or more) of the drivers don't have insurance. It's virtually impossible to get away with that (for very long) in NY. Get pulled over for no insurance, and your car is being towed away; it's treated almost as severely as a DWI.
Advice: seeing that you know who it is and where she lives, try contacting her local police agency. Give them the information that you've given us in the thread - how she's being a deadbeat about registering the vehicle and is accumulating a lot of parking tickets with absolutely no way for the state to enforce them against her. Perhaps they'll do something. (Well, unless you have useless police as seems to be the case in many ATOTers areas.)