FruitNut, I'm just a beginner. But, to my inexperienced eye I would venture to say one of the many Celeste strains.
I have heard from a lot of collectors that Celeste, for the most part does not have a breba crop. Or, at best a very small crop of breba. So with you getting that big a harvest so early in the fig season, I'm guessing your in the South, some where.
What town is the tree located? They look like they would be pure sugar.
Any pictures of the tree, to get an idea of how big it is?
Bob