I am doing a bit of homework on the Internet and it seems that only two steel reference 4445 have ever been posted. In total I see just 6 ever posted. Compared to 4445, there are many more mushrooms so 4445 could be one of the rarest. The so called Cassa Bariletto.

Correction: One steel turns out to be a ref 4443

 

Firstly, the number of examples that appear on the internet does not necessarily correlate to the number that exist. Watches that are desirable receive more press. As you know, mushroom-pusher 13ZNs are highly sought-after and so they are flaunted whenever someone gets a chance. A dealer may not even look twice at a beaten up ref. 4445 whereas a mushroom-pusher 13ZN in almost any condition would be collectible and likely find its way onto the web.

Secondly, rarity alone is of little importance. It all depends on supply versus demand. While any nice 13ZN is desirable these days, ref. 4445 is not particularly hot.

 

Can we get some pics? Not familiar with the 4445 reference.

 

These are 4443 Steel and 4445 Gold. I am pretty sure no other 13zn hooded models were ever created.