I do remember chasing trains over Cajon Pass in my '61 Beetle. With four beefy guys in the car it would tend to slow on the uphills so we worked out a routine. We'd all lean back into the seats and at the count of three we'd all lunge forward - repeat. You could actually pick up about 5 MPH doing that!
Mine was the same color as that '57. Only had that car for a year (bought used in '65) but it was probably the most memorable car I ever owned. Not all good memories. That 6-volt electrical system stranded me way too many times. And oh yes, the fuel lever. How many times did I forget to flip it back after filling? Reserve tank didn't do much good when you're driving on it.