I won't be surprised if the staff insists the sleeper passengers get off the train once it has reached its destination. After all, when you buy a ticket on Amtrak, you are purchasing
travel. Amtrak's duty is to take you safely to your destination, not to ensure you get your additional hours of beauty sleep. If a hotel tries to push me out of my room before check out time I might be pissed, since hotel is basically an
accommodation facility, but Amtrak is a
train, the fact that it happens to have sleeping accommodation is additional perk. Once the train has deposited you in one piece at your destination station, their duty is done. You are expected to get off the train. I wonder if anyone has tried (and succeeded) to get to stay on board for an hour or so after reaching the destination on a plane or a bus. I was once flying Lufthansa to Frankfurt and my flight reached FRA full one hour before scheduled arrival time, landing in sub-zero temperature at ungodly 5.15am. The flight attendants did not let anyone sit/sleep in the stationary plane for an hour simply because their "scheduled" arrival time was 6.15am. Megabus reaches their destination before time often (though I am sure nobody in right sense of mind would want to sit in a bus for an extra hour
)