You will not find the service available on the Railroads, in The USA. Not even AmTrak.
Years ago, we researched combining a group rail/moto trip, and contacted AmTrak, thinking it would be no big deal to haul our bikes in the baggage compartment of the passenger train. We even offered to palletize them, if necessary. We were flatly denied. They simply were not interested in hauling motorcycles on their passenger trains. Bummer, because riding the Southwest Chief from Kansas City to Winslow Arizona, and then meandering back home would've been epic.
As far as freight LCL (less than carload) on railroads, that went away decades ago. The various Truckload, Less Than Truckload (LTL) and express carriers (FedEx, UPS) began chipping away at that business beginning in the 1950s, and within three decades had it all. Railroads today only ship in bulk carload quantities for industrial and commercial customers. Long gone are the days of dropping a package with Railway Express Agency (REA) at the local depot, and having the railroad deliver it. REA has been gone since 1975.