In 1903 L.L. Whitman drove a Curved Dash Olds on that route SF to NYC in over 60 days...
along with John Hammond. There is a book about it https://www.amazon.com/1903-Curved-Dash-Oldsmobile-Horseless-Carriage/dp/B0006EIGKG and they went on to Boston, and Portland Maine, and then drove that Olds on the 1903 Endurance Run up through the Catskills.
The Olds had a single cylinder engine mounted horizontally under the seat.
Then he went cross country on a Franklin, which had a 4 cylinder transverse front mounted air cooled engine driving the rear wheels through a long chain. Went across in 33 days, half the time it took with the Olds
Supposedly the 1904 Franklin Type A Roadster which set the SF to NYC cross-country record of 33 days beating Packard's 64 day record. In the LA Natural History Museum and are not on display, but it was found to be missing a couple easily verified items that the cross country car had https://books.google.com/books?id=K_ELt1oimgIC&pg=PA222&lpg=PA222&dq=LA+Natural+History+Museum+1904+franklin&source=bl&ots=X3yKQ0CH2q&sig=4K7-IZSlPAFR331DK_3aRpeToS4&hl=en&sa=X&ved=0ahUKEwiH5_ikhL7RAhUpslQKHVTVCbcQ6AEIOjAE#v=onepage&q=LA%20Natural%20History%20Museum%201904%20franklin&f=false
As for cross country endurance races, the Franklin Company wrote to the then experts at the Automobile Magazine, and asked them to sum up the cross country races to their current time of August 16, 1906