I could beat myself with a stick.
Well, I finally figured out what it was that the Cumans would have been using for their leather armor... turned out I was simply barking up the wrong tree with my vocabulary.
~"they make farsetti of cordovano ....[in four layers].... and these are good for fighting in blah blah blah"
So sayeth Matteo Villani in his Cronica Nuova (highly abridged Armour Archive translation, 2005, year of the barking moonbat).
Well, hello, dumbass... modern cordovan is uberquality veg-tanned horsehide... medieval cordovan is tawed leather... likely of horsehide, but could be any number of things... which handily explains the following issues:
Q. Why does Villani use a term from clothing instead of a term from armor, you know, "breastplate" or something?
A: Because it's not cuir boilli, and so basically resembles nothing that the southern or western Europeans use for armor: it's just tough as old boots, quadruply so in this instance. So it's not an armored vest (a.k.a breastplate), it's a very protective doublet (a.k.a. multilayered leather caftan).
Q: If this is some kind of leather armor, why do the period images seem to show regular old flexible clothing or leather as their caftan?
A: Because tawed leather is as stiff or flexible as its maker wants it to be, that's why...
Q: Why is it made of lots of layers?
A: Because it's not tanned leather, and therefore doesn't harden the same way cuir boilli hardens. If it's glued together, the glue boundaries help resist damage via the Strong Effect, and otherwise, it slows a projectile down to where it then doesn't have the energy to defeat the underlying mail shirt, which is as fine as 15th-century glove links.
A2: Plus, it keeps the inner layers less likely to absorb moisture and de-taw as the alum salts wash out if it happens to be rainy, especially if they were curried before assembly.
There's more. There's lots more, from all the primary sources. And it all falls right into place. Oh, how I could beat myself silly by means of a stick with a nail through it.
Well, that's why we call it research, boys and girls. Eventually, you stumble onto the right answer...