In nyc, we show up at 9, the earliest check in, drop luggage with the porters, see it again when it comes to the cabin. The OP said they want yo drop off luggage, check in, and then explore. Nothing is out of order, no one had eyes on their luggage during the time between luggage drop off and boarding. If the all aboard time is at 2, sailing at 4, I can’t imagine why luggage can’t be dropped off early. While waiting in the cruise terminal we still see many disembarking, lots check in before the ship has been cleared.