Take the indirect route. If you are absolutely set on taking this trip by train, there are a number of options available to you. You can take 2 or 3 different trains the round about way to New Orleans. For example, you can book the Silver Star line from Orlando to Raleigh, NC, the Carolinian line from Raleigh to Greensboro, NC and then the Crescent line from Greensboro, NC. This will take a total of approximately 35 hours train time.
Take the train for only part of your trip. If you don't want to drive or fly, you can still travel from Orlando to New Orleans. You can take the bus to another Amtrak line and then hop on the train. For example, you can book a bus ticket from Orlando to Atlanta, GA, about 10 hours away. From Atlanta, you can book a ticket on the Crescent line into New Orleans, an approximately 12 hour trip. Altogether, that's about 22 hours of travel time.
Bite the bullet and fly. While you may be trying to avoid flying, this could be the best option between these two cities. Train travel without the Sunset Limited running is such a hassle, it's probably easier to just fly. Flights from Orlando to New Orleans only take about 2 hours, and when you book your ticket a while in advance they can be as cheap as traveling by train.
Drive to New Orleans. This is actually the fastest way to get there. It only takes around 9 hours to drive the 638 mile trip. If you don't have a car, you can rent one for a one way trip very affordably.
