I'm not instrument rated. However, I get my PPL at TEB 20 years ago, when they had flight schools, (first soloed at MMU). With the exception of the three majors, I have flown into and out of practically every airport in the area (currently FRG). Had I put myself in his situation and was diverted from FRG to JFK, I would have tuned the ILS and stuck it into JFK no doubt, before trying to make it to MMU or EWR with low fuel.
Practiced it enough times in X-Plane
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It was tough listening to the audio, but IMO ATC did an excellent job!