Or just rent a Pullman car. I have not actually reserved one, but I always find myself searching around for charter companies when I see these types of articles.
These guys claim $2500 a day for a charter. Not sure if it is legit or if there are other fees. (I assume you then also pay all the Amtrak fees). But I do have this on my back burner to try sometime. Since they offer some 4 bedroom coaches. Would be fun to get a group together to split the cost.