Ron Cummings sent me this photo & info on Barry Williams' "Porsche Special".  There are differences, but also similarities, between the two cars.

Given how racecar bodywork can change over the decades, is this car possibly the "Pignatelli"?

"Joe Playan thinks the (Paramount Ranch) "Porsche Special" is his Porsche 550 Spyder. He wrecked his car at Willow Springs. He subsequently took the car to Fred Ige, a fellow who was supposed to be able to fix aluminum bodies. He had a business, I believe, that was called Samo wheel alignment.  He had the car for 6 months and nothing was getting done. 

Joe took the car to Ernie McAfee on Sunset. Tom Bamford was the service manager. They had a guy by the last name of Carrel who worked on Ferraris and Maseratis. Joe asked him if he could get the car back together and running. He made that front end for Joe. He told Joe that the James Dean car was there and that he had used a few pieces off it to make Joe's new front end. Joe sold the car to Stan Sugarman, from Arizona. 

That is Joe at Paramount Ranch. This was the first time he had driven in more than a year. In the race Jay Hills crashed into the back of Joe. He was in a Porsche Speedster, Joe believes."

Ron Cummings on the two Porsche Specials:

"The Porsche Special, top photo, has nothing to do with the Paramount Ranch photo. The Special in the upper photo belongs to a friend of mine. It came from the midwest and doesn't have a Porsche frame.

The Paramount Ranch photo could very well be Joe's first Spyder after the rebuild.  However, that car is listed in the race program, March 1957, as John Porter's 550 Spyder.  But Porter's car never looked like that.  It was always a near-concours car. I don't think that the Paramount Ranch car is Porter's and may be, like you say, Joe's car. Could this have been a different Paramount Ranch date?"