The Southwind (renamed the Floridian) was an original Amtrak train on day 1, which changed routes several times. It lasted only eight years.
The idea others have discussed is run the CZ and let LA passengers transfer to the Coast Starlight (for now, later to the CA HSR)in CA.
Setting the record straight on the Lake Shore: initially on May 1, 1971, an unnamed train ran on the Lake Shore route only from NYC (GCT) to Buffalo. Nine days later on May 10, 1971 it was extended to CHI.
The North Coast Hiawatha also started on June 5, 1971 and was dropped in 1979.
As Don Oltmann said, Amtrak has preserved much and also changed a lot over the 43 years, adding dropping trains and changing track routes. “Amtrak’s original system was made up of 19,233 route miles covering 43 States and the District of Columbia. By the end of 1971, the system had grown to 21,528 miles. In 2006 Amtrak had a system of 21,157 miles, in 46 States. Since 1971, Amtrak has abandoned a total of 14,075 miles,” http://cs.trains.com/trn/f/507/t/57085.aspx