I'm surprised the eastbound Capitol Limited to the southbound Silver Star, doesn't have a guaranteed connection. And I hadn't checked the historic Amtrak timetables to see what the Sunset schedule used to be like east of New Orleans, but for the most part I recall years ago(and still today) that you have to overnight in New Orleans, to do any train connections. You're right that it probably be much of a net positive to travel 59 to 1 eastbound(you know, east of New Orleans) theoretically, unless you had to go to Mobile or western Florida on the panhandle.
Sigh, I was under that mistaken impression for all this time that there was a guaranteed connection between the Cap Limited and at least whatever Silver train leaves DC later, to head to FL. Guess not.