This post is 100% on the ball correct. Herein lies the real blame for what happened that day. Our hands are tied too.
Min fuel doesn't mean squat to JFK ATC. The FAA management is forcing the controllers to over-maximize the traffic into and out of JFK due to the runway closure. In retrospect, maybe the best course of action considering that it's obvious that the airline and FAA managements want to put the runway closure monkey on the back of the pilots, would be to divert when the FAA insists on landing aircraft on runways with close-to, or blatantly out-of-limits winds and refuses to allow you to land into the wind.
As usual, it's the pilots that have to make up for the lack of leadership in airline management and the FAA.
If you read what the FAA controller rep said afterwards, it's obvious to me that the controllers at JFK are under tremendous pressure from FAA management to "push tin" to the max and to hell with everything else.