You can hire a private rail car: https://www.amtrak.com/privately-owned-rail-cars

Well your link is to have Amtrak tow your private rail car. You have to provide it yourself. There is a different company that offers luxury private cars that I can’t remember the name of now.

There’s a number that provide rentals (many are preservation societies/charities that hire out their cars for income).

https://www.aaprco.com/charter-a-private-car

Of course, if you’re really rich, you’d have your own. ;)

If it's continental, having a driver and a comfortable car would go a long way then.