Congratulations on your figs graft success, Drew. You are reaching the same conclusion i reached last year. If i want to secure a rare variety the best way is grafting.
Regarding the pictures in this thread. If i hadn't such good varieties grafted myself, i could be getting some fig envy of you guys. Nixgardens, that Lebanese fig sure looks interesting.
By the way, thanks to a good friend, i was able to get my hands on one cutting of Lebanese Shiani (Shiagi?) from Pons collection. He told my friend that he likes this variety very much. I did several grafts with the cutting.
In the database in his website, Pons doesn't have much information on this variety, apart from the origin of the cuttings - he got them from the USA in 2010.
http://www.sonmutnou.com/el-camp/detall/972
Could it be one of the varieties you are mentioning in this thread?