We rode the New York Central 3, a private car built for a Vanderbilt a century ago, cross country, attached to the rear of the Lake Shore Limited, changing in Chicago to the California Zephyr. A great experience, watching the scenery go by for 4 days, with a 270-degree view from the sitting room in the rear.
Basically, there are hobbyists who buy and upgrade these cars, and try to break even on chartering trips on them. They’re clearly never happier than coming along for the journey (you need an official liaison on board anyway to interface with Amtrak staff) and fixing stuff along the way.
This particular car sleeps 8, and it cost us less than 4 couples taking a cruise from Fort Lauderdale to Los Angeles via the Panama Canal, and less than booking a private jet that seats 8, but more than first class airfare for 8 cross-country.
And it also depends on whether they find someone to book (some subset of) the return trip that will start within a day or two of your arrival; otherwise you have to cover their Amtrak fee for the dead-head return. I’m told there’s a network of enthusiasts who watch for such possibilities. Rather, two networks, who hate each other for no discernible reason. Or that’s how I understood it, as an outsider getting a glimpse of an obscure but intense sub-culture.
Since drfuchs hasn't answered yet, here's a figure from 2011:
"Not up for chartering your own car? Then perhaps you'd like to take part in an arranged tour. There are several vendors that offer trips on private varnishes. For example, Palm Leaf LLC is offering a week-long trip by train from Los Angeles to New Orleans for Mardi Gras. While in New Orleans you can continue to use the train as your hotel, parked right in the middle of the action. The tariff? $2,995 per person for a single room, including meals while in motion."
Basically, there are hobbyists who buy and upgrade these cars, and try to break even on chartering trips on them. They’re clearly never happier than coming along for the journey (you need an official liaison on board anyway to interface with Amtrak staff) and fixing stuff along the way.
http://www.nyc-3.com/