If I go by the F4F gallery, I think St Anthony would be a no, Kadota is a possible, Marseilles is a possible. The one unique characteristic of this fig I'm not seeing elsewhere is the area around the eye. It's almost like it has a 3mm-thick ring (like a fur cuff?) around the eye, whereas many other figs eyes look almost like the top of a blueberry (like torn paper, you know?).
Look at the first picture above, you'll see a blurry idea of what I mean. Maybe in the 3rd pic also. ALL of the figs on the tree are like this.
Oh, and John, thanks for the well-wishes. I don't know if this is worth propagating or not. It doesn't seem to fruit a ton of figs for the tree size just yet, and the fruit seems to bruise/scar a lot, so if you like your figs looking nice and blemish free, this wouldn't be something you'd want to grow. The best tasting fruit looks really beat up, almost insipid/rotten.
Ever since I ate the whole one pictured, which produce NO sap (er, latex) when pulled, I've had this tightness in my throat that happens when I accidentally eat a drop or two of sap. I was very careful to totally wash before eating, in case they contacted the leaf too much.
I will be keeping my eyes on it. It's amazing not to find a Celeste - this is one block due north of the "Unknown Hobart" I've posted about and been handing out cuttings of (big red pulp, yellow-green skin). The fruit size on that one is about the same as this one, but that one is blood red inside, this one is honey-colored inside. Eye is about the same size on both. Leaves are smaller on this one.