Hey I'm also from Connecticut and would love to get some cuttings from this tree if you are able to (im willing to pay obviously). It'd be nice to know I would have a tree that is almost guaranteed to grow in my area (USDA says 7a, but who really knows).
In terms of identifying this fig, I can't really offer much of an answer because I am relatively new to this. I can say that seeing it was brought from Italy to Connecticut, it is probably some sort of Southern Italian variety (most Italians to US came from south). Also, seeing it survives our winters, it might be some sort of Mt. Etna variety? But I'm just speculating here, could be some rare Italian variety from another cold area for all we know!