A friend and I recently traveled ATL-WAS-CHI-CVS-ATL, on the nb Crescent, wb Capitol Limited, eb Cardinal (only runs some days), and sb Crescent. (Actually we started and ended in Anniston, but that doesn't matter for your purposes.) Four nights in a row on different trains, and nice daytime layovers of several hours in DC, Chicago, and Charlottesville for a little bit of sight-seeing. As others have posted, much longer trips are possible, but this was a very enjoyable and easy trip.
Throwing a return route into your itinerary may give you additional options, if you can do them on different trains as we did. I think you can visit a city twice on a railpass, but I haven't looked at the rules in a while.
If so, using the above, you could stay on the sb Crescent through ATL to New Orleans, overnight there, and then continue from NOL on the CONO or SL (only runs some days), with various options from there. Have fun on your trip!