In my area of California, figs have been grown for generations, in part, due to the importation of individual caprifigs, from overseas. When I researched this on Youtube, they were hand carried, from orchard to orchard, and hung by a string, like necklaces, on trees, which needed to be pollinated. There is no need to have an entire tree, per se.
I am not formally educated about this, but, to the best of my understanding, the harder, small figs, with gnat-like insects, do occur in the driveway, near my house, without any human intervention.
A local store sells 'Turkish Smyrna' figs, which are white, but this alleyway tree has purple-skinned fruit with red flesh.
So, I am assuming that the variety does not strictly have to be Smyrna, in order to bear caprifigs.
Do any kind of domestic figs, at all, grow near your house?
My ordinary fig seedlings developed fruit without any extra effort being taken, on my part.
I have an interest in Bible plants and have come across a potential, alternative method, which may have been used on sycamore figs.
You see, they apparently stay hard, on the tree, just like what you are describing. The pollinator is not known to exist in Israel, at least not today.
It used to be considered among the humblest of jobs (for someone like Amos) to repeatedly prick, bruise, or oil the skins of these figs. This would apparently cause natural ethylene gas to be trapped inside of the fruit, resulting in something more palatable.
