I totally understand your frustration. Ahhh, if only they were as easy to sex as Zebras or Cut Throats...etc.
I know you didnt ask for advice lol, but I've had a bit to much coffee today so here it is
This may, or may not benefit you, but here is what I do with my Societies: Generally, I buy at least three at a time and I make sure they are easy to tell apart by markings and color. I then put them alone in separate cages so that they can only hear each other. I do this for a few days. After that, I introduce them one at a time....sit back, watch and wait. Since they have been apart, your males will
usually start singing right away and hens will sometimes crouch down.
Another method I use to help sex societies in by looking at their beaks. If you have a true pair, take them side by side and examine their beaks (for reference). You should see a slight but definite difference in them.....the hen will have an overall slender, less bulky bill (and head) than the male. I
especially look at the underside of their beaks where the lower mandible meets the throat.....on females it will be more "U" shaped and on your males it will be more of a "Y". After a while, you can spot them pretty quickly with this method...but I still look at my true pairs side by side every now and then for a refresher.
Again, I know you didn't ask for Society sexing tips...haha, so sorry if it wasn't needed.
Best of luck finding an actual hen!