In 1933, the 12-cylinder Pierce-Arrow cars were given model numbers starting with "12" and ending with their wheelbase, such as 1236, 1242, etc. IF this car is, in fact, based on a 1933 Pierce-Arrow V12 it would be (judging by the extreme wheelbase) a model 1247 as Craig stated.
Bear in mind that not all of the signs in front of the cars in the Harrah Collection were always 100% correct. I recall a visit there in 1976 where I noted more than one error. In the case of one-off cars that were called whatever the builder wanted to call them, the answer could be anything. . . . But in the case of a Pierce-Arrow, the factory model designations are well-known and well-documented. Most sources say that David Kouri's "speedster" is based on a 1933 Pierce-Arrow V-12. That makes the original Pierce model number of the car it was based on pretty easy to determine, and it looked like that was what you were asking for. As a 1933 Pierce-Arrow 12, it HAD to be "Model 12XX". Maybe it isn't a 1933 after all? Curious.