I reckon EK201 has more seats and thus a higher chance for D class to be released. Can you take the later flight to JFK? Means more time in the new lounge

Set up an alert on ExpertFlyer.com and then see what happens. If it doesnt come thru prior to departure, ask at the lounge and then ask at the gate. Make sure everyone knows you want to use miles and you are on the list - also call several times and see if an agent can do anything.