Figs in pot do that when anything was missing at one point or another,and easdpecially when young.
If you do not want fruit drop,let the fig grow roots in ground trough the draining holes.
Of course make more holes on bottom side of pot,for drainage and aeration.
I do not care how much you take care of your fig in pot.
You need to forget to water once and fruits will start falling out later.
Letting the tree go inground to take what it needs is the answer.
As a matter of fact I know Texas Mission does not drop when in ground.,because I had fruits from it in the Past.
As for being inpatient to get ripe fruits.
Young plants get fruit ripe much later than the cultivar will do when mature tree.
My older trees started getting ripe on the 10th,of August.
Your young trees will get ripe this year started September 1st.