I had some success in the past in getting an earlier flight out of JFK with a non fully flexible ticket. JFK is a bit special as for some period of the year they will have a lots of heavily overbooked flights. Therefore they know that if they can fill a bit more an earlier plane they will do it.

you can check if your plane is looking to be zeroed out and if the earlier plane seems to offer more availability which could give you hope to succeed in getting an earlier plane