Actually I found mention of it in the 4/5/92 through 10/24/92 timetable. Page 50 shows the Capitol Limited with a thru Chicago to Miami coach, exchanged with the Silver Star. No mention of a sleeper.The concept would have died, if not already dead, when the Capitol Limited went Superliner. That changes everything.According to the 4/29/79 timetable, the Floridian would leave Chicago at 9 PM on day 1, and arrive in Miami at 1:10 PM on day 3. A bit less than 40 hours to get there. It now, going CHI to WAS, takes 46, via the Capitol Limited and Silver Meteor.
Now then, we can honestly come close to that time, say 40.5 hours, creating a tri-weekly "Floridian" running CHI-WAS-MIA with 3 P42s, 3 CCCs, 3 Trans/dorms, 4 sleepers, 4 coaches, and 4 coach baggages. Here's how it works. The Capitol Limited on those three days runs P42, Transdorm, 2 WAS sleepers, CCC/Diner, SSL, 3 WAS coaches, 2 FL coaches, 1 FL sleeper. At Washington, the CL breaks up short of the station, decoupling the 2 coaches and one sleeper, then pulls itself into the station. A single P42, coupled to to a CCC and Trans/Dorm, backs up to the other 3 cars, couples, then pulls into WAS. It then leaves shortly along the Silver Meteor route.
The train gets to MIA, and turns for the next day. The train then goes back to WAS, uncouples its CCC and P42, and gets reattached to the CL. In essence, the three CCCs and Trans/Dorms short turn in WAS. For servicing, they could be rotated into the CL.
That might be a good idea,with what we have to work with.
But keep a couple of things in mind, in case you do not already know them.
One,I believe for a brief period of time there was through CHI-MIA equipment on that route. Perhaps it did not work well.
Secondly, just for a little historical perspective, when the South Wind--later called the Floridian-- (and two other trains, the Dixie Flagler and the City of Miam) were placed in service in 1940 they took just over 29 hours. That is about eleven hours faster than the Floridian eventually had to take.
Maybe that does not matter anymore. I am not sure if Amtrak is still trying to sell some concept of "speed" for LD trains. The intersate highways put the trains on the back seat for speed even back then. So much padding, trains like the Sunset Limited, so much slower than they used to be. Maybe taking that much longer isn't too much of a problem.
Who knows?
Anyway, I'm something of an Amtrak historian. I've never seen through cars on the Capitol Limited.
My timetables for that period are currently scattered around so I did not try to find the timetables before and after these dates. I do seem to recall that this thru service was dropped by the time I had heard it had started.