Not sure if anyone else has said this, but you may be able to take the earlier flight with no additional charge or hassle.
NCL owns the 'reservation' but I know from experience that if you have a direct flight (no connections) and show up at the Delta airport counter on the day of your flight, they can and do allow you to either move your reservation to an earlier flight if there is availability, or put you on standby for an earlier flight so you can try to get home faster. We have done it twice now using NCL's reservation. The agent at the counter was more than happy to move us both times.
They won't do it ahead of time, but once you show up at the counter on the day of flight? Delta can and will want to fill seats on an earlier flight if they can.