According to the QRH, using F40 for landing only saves a few hundred feet of runway over an F30 landing. If the FO, had no experience of F40 landings, a wet La Guardia, was not the place to try it. It was the long landing that caused the overun and it sounds like the MEL'd speedbrake was extended late and the late reversers may not have helped.
The real issue is why the long landing occured and was not noticed by the FO and the go around not called by the Captain. Two engine go arounds are not well taught in my airline and there is no shortage of evidence saying that they are a real problem on the B737. There are so many possible go around scenarios and you have think out how you are going to carry out each one without scraping the tail, stalling out, nose diving in, overspeeding the flaps etc.
If go arounds are not well trained, "hoping" that the aircraft will stop will seem like the better option in the heat of the moment....like in this case.