My 1983 E series American P has been my main bass for years. Mine has a 1.75" width.
You might be getting mixed up with some of the Squier E series basses. I had a Jazz that was made in Japan. The neck was awesome (I still have it). Later I think the E serial numbers also were used for some of the Korean made basses.
My experience has been good with both the American and Japanese E series instruments. Let us know if you get it!
chris