I was hoping that someone would answer this. I also have a young Kadota that is still making figs.
Since nothing was posted, thought I would just let it go and see what happened.

Some will make it and some won't. Closed eye figs tend to over winter better. This is because open eye figs tend to sour. This happens because an insect enters the eye and deposits yeast inside the fig. When the yeast ferments the figs sours and becomes unpalatable. During the winter the open eye is seen as a nice cozy place for insects.

I have the same problem, my Turkey Brown that was chewed to the ground by a dog last year is now about 5 feet tall and it has a bunch of figs on it. I sure hope they do ripen. I'm thinking of trying the oiling trick.

greendesert the oiling trick as you call it has its limitations. It only works on figs that are at the stage of development where they are just starting to swell or later. Also temperatures still have to be warm. My guess is you are fast running out of time as it will not be warm here much longer.