I think departing around 7-8 and arriving 6-8 is optimal.
I agree about arriving, but I think the ideal departure would be to open for boarding around 7-8 but not close boarding or depart until about midnight, to allow people attending concerts, shows, night ballgames, etc. to get to the station. Admittedly, that ideal maybe can't be achieved where trains can't tie up a platform for a few hours.
I'd love to see a fleet of dedicated night trains, distinguishable from long-distance trains by having
(1) no dining car, but a cafe for snacks and drinks pre-sleep and coffee/tea/light breakfast on arrival.
(2) 1-2 coaches with ordinary seats. 2-3 coaches with very reclinable seats, but mostly sleeping cars focused on providing ample single and double occupancy. Capsules as on the new European trains for single riders. Lots of roomettes for couples. Few bedrooms. One common shower per sleeper car. Some luggage space, and definitely bicycle capacity, but not too much luggage space.
I picture these trains used on a series of night routes, making stops along the way (hence the ordinary coaches) but timed and mostly focused on the end point cities (and a suburban stop or two). Groups of routes radiating from central hubs that are major destinations and have enough "secondary" cities at the right 5-10 hour range: Boston, New York, Washington, Raleigh, Atlanta, Orlando, Chicago, New Orleans, Dallas/Ft. Worth, Los Angeles. Would have to have enough capacity that the round-trip fare would be competitive with round-trip day travel + hotel room.