Not to mention price, I understand there is no 4-string Adam Nitti model.You could look at the Ibanez Adam Nitti model which has Seventies Jazz pickup spacing and a two octave neck for just under $2k.
I can get kinda Jazz sound even from my BTB. But I want the look.The Ibanez models with Nordstrand single coils can get you pretty much the Jazz sound without the Jazz look.