The only thing that will fix this is the Reagan approach. Fire all of the striking workers then set about replacing them.There will be more discomfort than an immediate cave will induce but it won't happen again. That would take a Giuliani as mayor and NYC doesn't have one of those any more.
Fire 10% of the work force each day they are out. After 10 days offer to hire them back at 50% increase in salary provided they contribute for their own health care, contribute for their own pension, retire at 62 and give up retiring at 1/2 pay. In addition, the State will fund immediately 50% of the 1/2 retirement pay into their pension accounts.
That should break the union.
NYC should turn over the operation of its transit system to several private companies after competitive bidding.