Martin makes tons of "signature" guitars, the ultimate design of which are the results of collaboration between the signature artist and Martin representatives. Here is a page from Rory Block's site about her Martin model:
http://www.roryblock.com/Pages/Page Links/Martin.htm
Evidently, these models are not replicas of instruments the artists played, but rather are instruments that have custom features desired by them. We don't know, or at least I don't know, how much of the design of the Iz model comes from Marlene's input and how much was a Martin decision.
Some of the discussion in this thread assumes that an "artist" model "should" be as exact in every detail to the instrument the artist actually played ala the Aldrine model, but that clearly is not Martin's idea. Some of their signature artists are not even known as guitarists; some of them who are did not typically play Martins, or so I have read.
I wish Martin would make more "signature" ukuleles in tribute to some of the fine Martin ukulele players around these days. I would be delighted to see an Ukulelezaza Style 3, or a Winin' Boy D-shaped, Style 1, particularly if these guys got to pick all the features. Heck, I might even be inclined to buy a couple.
As I wrote before, I also wish they would make the Style 1 again as it was made before they first stopped making ukes. That way, those of us on the forum who want to play an instrument like Iz played, or Ike played, or Peter Moon played, etc., but didn't want to go vintage, would have that option.