It would be neat to find a Trains article, if there is one, about how the cars were transferred. Here’s an article from Central Headlight, April 1946.
First Coast-to-Coast Service by the New York Central
Two Routes to Los Angeles and Two More to San Francisco Receive Warm Public Welcome
The first through daily coast-to-coast railway passenger service between New York and Los Angeles and New York and San Francisco was started Sunday, March 31, by the New York Central and several western railways. This is the first regular daily standard Pullman sleeping car service on the United States railroads that permits trans-continental travel without change of cars.
Two routes to Los Angeles have been established. The first, utilizing the Central’s famous 20th Century Limited in conjunction with the Santa Fe’s Chief, was announced March 20, by G. Metzman, President, New York Central System, and Fred G. Gurley, President, Santa Fe System. A few days later, announcement of an alternative service, utilizing the New York Central’s Iroquois and the Los Angeles Limited was made. The Iroquois also carries a car for San Francisco.
Still later another service, each way between New York and San Francisco, on alternate days, using the Central’s Commodore Vanderbilt and the Exposition Flyer, over the Burlington, Denver & Rio Grande Western and the Western Pacific Route, was placed in operation. This service out of Grand Central Terminal, New York, started April 4 .
On the first day of the new service, the 20th Century Limited, leaving New York at 5:30 P. M. included an all-room sleeping car which, upon arrival of train at LaSalle Street Station, Chicago, at 9:30 the following morning was delivered to the Dearborn Station, where it was attached to the Santa Fe Chief, leaving Chicago at 12:01 P. M. and arriving Los Angeles 11:50 A. M. on Wednesday, April 3. Eastbound the Santa Fe Chief, leaving Los Angeles Saturday, March 30, at 12:01 P. M., similarly included an all-ro