I believe all 22 are smyrna and found in southern, Iran. While the article is in Farsi, the key chart is translated... skip to page 6 Table 1. Fruit size, exterior color, pulp color, meat color, cavity size, seed, acidity... all documented.

To summarize... with loose name translations in parentheses for any I could... some of these are made up words or local slang or village names so I have no idea...

The variety names are:

Allamee (tall/skinny)
Matti
Kashkee- *striped* exterior, red pulp, no cavity
Barg-chenari (oriental plane leaf),
Rownoo
Sabz (green)- the majority of the bone dried figs made from this, pink interior
Siah (black)
Shah Anjeer (king fig)
Kounoo
Charmee (leather)
Torshook
Kanezak
Pariyovee
Asalee (honey)
Aghaiee
Kharfak
Ghanee (rich)
Manbilee
Payves
Mati-Siah
Siah (black)
Mati Sefid (white)

PDF with full chart

I was hoping for the american alphabet Farsi, not the script. 

page 6 Table 1 the English fun starts!