I just reread the captain's report of what happened. When they diverted north of ALB to JFK at FL350 they had no reason to shut down an engine but conferred with mx and decided to go to JFK because of the thump. Descending for the arrival at FL220 the engine problems started resulting in a shut down. The captain was consistently considering other divert airports but considered JFK his best choice at that time. Very professionally done in my opinion. He landed 15,000 pounds overweight because of time limitations so landing before JFK would have made a heavier landing which must also be considered. Familiarity with an airport and weather also dictate what is the nearest suitable airport.