Fig hybrids are produced by "hand" pollination. You want to use an "edible" male capri fig as the pollinator. I have seen a written procedure once but do not recall where I saw it. I might have it on my other computer. As best I recollect, it was not written by Condit or O'Rourke. Injecting a 50/50 alcohol/water liquid slurry of male pollen using a large bored needle syringe should work. The hard part is finding a good edible male capri fig. LSU had a good one known as "Yellow Pollinator". I had a young start once but no more. Yellow Pollinator produces edible figs in May in my area. For comparison as to how early that is......regular Celeste starts producing about July 1st in my area. Do you see why I was interested in growing it?????

Rather than try to breed new figs (which I did think about doing), I have found it more rewarding in finding more of the LSU "lost figs". Many of O'Rourke's initial "selections" were lost when funding for the breeding program was halted. There are still some little known O'Rourke selections in my area. I have some of those in my collection without any name. Since they all came from either a Celeste or a Hunt mother, they ALL deserve further study. I am the right guy to do the studies. They ALL have good potential because of the excellent fruiting traits of their mother that hopefully were transferred to the offspring. I have one that I believe is a Golden Hunt. It has the same exact shape as a Hunt fig; but, it has a beautiful golden color rather than brown. Time will tell......

Dan

For a basic primer of what people like Dan are doing to breed new figs, see The Weird Sex Life of Figs at Ray Givan's fig site.

Here is a link that might be useful: The Weird Sex Life of Figs

Fig breeding is a very long-serious-laborious matter.
A good outcome is often against the odds (good luck!).

Good (old) fig breeders I know about are:
University of California (UC[D/R]) and LSU in Louisiana.
Male pollination (caprification) for this non-fruit/inverse-flower
"fig-thing" is needed. This is naturally done by the fig-wasp entering
through the fig-eye.
Yeah - that is why nature made that (in)famous tiny-hole fig-eye for!!!
The fig-wasp is natural in the Euro/Asia temperate regions.
In this USA, I know that it was introduced only in some parts of California.
(Just Google for Smyrna/CALmyrna fig history)...

For the better Common-Fig no-caprification-required and desired by us North fig people;
rather than the San-Petro/Smyrna fig types; choose a "persistent" male caprifig
specimen (also touted as edible, by humans; not just goats).

UCD has at least two:
UCR-228-20 (Enderud)
UCR-271-1

As a side line - most known figs in the USA were
brought here long ago by migrant people as twigs in
their suitcase from what is now the EU...

Forgot to mention one other important thing.
Once a common-fig is bred; how does it perform?
Properties?
Is it sweet, prolific, etc.

These FFs are mostly about discussing the properties of
many long time multiple/confusing/named existing figs...

Persistent (or Common) figs which do not need pollination to set crops. These are the kind home gardeners most commonly grow. Examples are Black Mission, Brown Turkey, Celeste, Brunswick and Adriatic.
===================================================
This is a relief.
I hope Black Jack, Hardy Chicago and Italian are included in this group which does not need pollination.

Black Jack and Hardy Chicago don't need to be pollinated and, although I'm not sure what it is, Italian almost certainly doesn't either.