At one time Richard Rawlins of Gas Monkey ( may have been with his friend Dennis in a Jaguar I think ) held this record of 31 hr 59min.
Many moons ago I read Wilt Chamberlin's autobiography. For fun on his summer's off he would take his Bentley and go across the US before this Cannonball Run ever started. He would be by himself and it was for his own fun. I seem to remember is best time was in the 33 -34 hour mark. I am not sure if he enjoyed this record the most or the 20,000 women he claimed to have bedded.
Chuck
Personally, anything not documented by witnesses about Wilt Chamberlain is pretty dubious.
Putting it clearly, I have my doubts.