That must've been one helluva an expensive taxi ride.
Yes, it probably cost them some bucks, but the Amish are known to be prosperous people. What they were doing was akin to cruise ship passengers arriving in a port and hiring a driver for the day to take them to various locations. They were probably going to at least one of our other two National Monuments in the area. Sunset is about eighteen miles from downtown Flagstaff. I don't think I have ever seen the Amish in Amtrak sleeping cars - but they travel by coach in considerable numbers. Two years ago I encountered two young Amish men from Indiana who were traveling the West by train and they were having a fabulous time. It is also common for them to be on the way to Tijuana, Mexico, for medical care.
I've seen Amish in sleeping cars.
It's odd but it usually goes like this:
Most elder 2 from the family (usually grandpa and grandma or mother and father) gets a roomette and everyone else travels in coach, and they adjourn in the Lounge Car.
That is likely the case. I have found them great fun to talk to in the lounge car. They can be quite friendly but usually need to be spoken to first.