I've sailed Anthem and Quantum many times form Bayonne and the uploading 4k+ passengers is pretty quick. As an example, disembarking on my February sail, I was assigned an 8AM slot. Took me 15 minutes from ship to luggage, Customs and street. Customs in the US uses facial recognition technology and make the process so much easier. No forms to declare or showing of passports. In my car a few minutes later and home by 9AM. I'm about 25-30 minutes from cruise terminal.
Ps. Same time frame even with Oasis which has 6k + passengers.