Montgomery, AL to Minot, ND. WOW! Now there is an origin and destination pair that we do not see very often.
Here’s the problem. The best Amtrak route from the deep south to Minot is New Orleans overnight to Chicago, and then Chicago overnight to Minot. The trick is getting from Montgomery to New Orleans by any Amtrak mode.
There is a train three days a week from Mobile to New Orleans, but there is no bus connection from Montgomery (and the train leaves Mobile at 4:25am, ouch). There is a daily train from Birmingham to New Orleans just after noon, but there is also no bus connection from Montgomery, and the train gets to New Orleans after the Chicago train has left. You would have to overnight in New Orleans and take the Chicago train the next day. That would be a three day trip. If you use the Amtrak web site, they will route you via bus from Montgomery to Atlanta, train overnight to Washington, DC, another train overnight to Chicago, and a third train overnight to Minot. That is another three day trip.
A sort-of reasonable Amtrak option is to drive to New Orleans, and then take the two-night Amtrak option New Orleans to Chicago to Minot. But Montgomery to New Orleans is not a short drive, and then you have to stash the car in New Orleans until you return.
My suggestion is this. Drive to Birmingham. Take Southwest Airlines (cheap!) from Birmingham to Chicago, arriving late morning. Trek downtown to Union Station and take Amtrak overnight to Minot. Returning from Minot, Amtrak-it overnight to Chicago, and then take a late Southwest flight back to Birmingham. This will limit your cost, and will also make your travel time reasonable.