Well, if I absolutely had to get to point B by a particular time, I would want to have checked out alternate airline or bus connections beforehand, including the availability of a short hop flight or bus connection from an intermediate stop on the first train to an intermediate stop on the second train, if any existed, or maybe a commuter plane hop from the first train's destination to an intermediate stop of the second train, and then make the decisions enroute, based on how late train #1 was and Amtrak's estimate of whether train #2 was going to depart on time. If there's a meeting you have got to make, you NEED a backup plan, is what I would say. Even if Amtrak said they would guarantee the connection, I'd be keeping track by cellphone and be prepared to launch the backup plan, with the paperwork, telephone numbers, and printouts for all of that in my carry-on and kept with me at all times. Do all the research ahead of time so you know exactly what's available, where it is, and what it would cost. If nothing else it will give you peace of mind while traveling.
Bottom line, though, I would probably have given myself a one-day pad, to arrive in the meeting city a full day ahead of time. If the trains make connex and get you to NOL on time, you get an extra tourist day in NOL, which would be nice. If not and you're a day late into NOL, you still make the meeting. Much as I love riding them, long distance trains are not conducive to travel for meetings on a deadline, unless you can give yourself a sufficient schedule pad for peace of mind or you have alternative transportation lined up just in case.