You don't need award inventory to be available due to a cancelation/rebook like this. You just need available seats on the plane for your JFK-HNL ticket.
The problem is, as you saw, things are packed. Looking at EF also, I see nothing for the NYC area to HNL for tomorrow... next availability is Sun LGA-MSP-HNL but C+ is showing 0 and its only Y2 for the LGA-MSP leg. There are open/unassigned C+ seats on both flights however.