If you could get the average speed up to 55 mph (approximately equal to the SWC), you could get a schedule like:
Chicago 8:50 AM 5:00 PM
Indianapolis 6:15 AM 9:30 PM
Louisville 4:10 AM 11:40 PM
Nashville 12:20 AM 3:30 AM
Atlanta 6:50 PM 9:00 AM
Jacksonville 12:45 PM 3:10 PM
Miami 6:00 AM 9:50 PM
By sacrificing reasonable service times at Louisville and Nashville, this schedule creates a business-friendly overnight timing between Chicago and Atlanta and a very long day train between Atlanta and Miami. It also only uses three train sets. Realistic? Probably not... but we can dream, I guess.
I think the question is whether this train is scheduled more for end to end traffic or the intermediate markets. If you want to bring back service to areas which haven't had service since the late 70's (Louisville and Nashville) then having it scheduled during the graveyard shift is going to be a hard sell to these areas (or you can use the theory they will be happy just to have a train).
Looking at the gaps between cities not counting JAX-MIA (ORL is in the middle), the largest gap is between ATL-JAX. Ideally the graveyard shift would be between there but a 6am arrival into JAX puts it pretty close to the Silver Star (although if it skips TPA it would arrive MIA significantly earlier than the SS). There is a 5.5 hr gap southbound (not counting the time difference) between ATL and Nashville but that would put it either after midnight on one end and/or before 6am on the other.
The ideal southbound schedule in Florida to give passengers a choice in times would either be the proposed schedule arriving in ORL/MIA at night (but leaving Louisville and Nashville in the dark) or to arrive in ORL early and MIA around lunchtime (it would help train to cruise traffic which I have heard some are looking for). That would put JAX in the graveyard shift but that might not be as bad since they have two trains already (but any possibility of ATL-JAX traffic goes away). If you flipped the southbound schedule 12 hrs that leaves CHI at 5am. Push it so it leaves CHI at 7am you get Louisville 11:30AM, 1:40PM, Nashville 5:30PM, ATL 11:00PM, JAX 5:10AM (not too bad), MIA 11:50AM (assumedly ORL around 7:30-8am). Then CHI-ATL becomes an all day affair with no chance to sleep it off so that would hurt business between the two cities.
Northbound if you flip it 12 hours you get an evening departure from MIA (current Silvers are both morning) with only JAX during the graveyard shift (and 12:45am isn't that bad). Again, ATL-CHI is an all day affair.
Other than Louisville & Nashville, the other potential I see is ATL-JAX-MIA service. The schedule suggested between ATL and MIA would fit very well with the Crescent, perhaps as through cars (southbound can always be pushed back but northbound could be a problem unless you put MIA before 6am). Of course considering how things are in ATL now good luck with that.
Trains Traveled: Broadway Limited (CHI-Harrisburg, PA), Three Rivers (Harrisburg, PA-CHI, Altoona, PA-CHI, PHL-CHI), Capitol Limited (CHI-WAS), Lake Shore Limited (NYP-CHI), , Silver Meteor (PHL-ORL), Southwest Chief (CHI-LAX), California Zephyr (CHI-SLC, SLC-EMY), City of New Orleans and/or Illini (CHI-Champaign, IL), Soon: Texas Eagle (CHI-DAL)
Bring back the Broadway Limited (or Three Rivers or any Chicago-Pittsburgh-Philly train)!