I was on the June 19-27 sailing. They offer luggage tags for you to pick up at a designated place & time the day before disembarkation. (For Platinum, they brought tags to our cabin with instructions to meet in one of the dining rooms.) They also encourage people to take all their own luggage down (that for me is a first—it may be due to limitations in how much luggage the terminal can hold), with the requirement that you meet at an earlier time than the first of the tagged groups. As it turned out, there were just too many people on board for disembarkation to keep to the schedules, and it all backed up.
At one point they halted the exiting for a time to restrict numbers in the terminal. Once in the terminal, it was very quick. I think your six-hour window of time will be sufficient for getting to Penn or Grand Central.