OK then!!
Up for the great Finale!
The screw is out!
Much easier than expected, although this thing is sitting on my shelf for more than two months now, and I had several previously failed attempts.
What I did now: I lightly heated the knob, and then use a light hammer to tap it. A couple of days ago I had sprayed the hole with penetrating oil. After it colled down, I used 4-5 different flat headed screw-drivers trying to "feel" if the screw was moving. Then as I was getting ready to go to the epoxy-drop solution, the screw come out as if it was never stuck!
As you can see from the pictures, this is not a botched screw, it's just a piece of screw that a technician or ex-owner put in place to keep the knob on the shaft, because he had lost the original piece. That's my assumption.
Now that I see the extracted part, I consider myself extremely lucky that this turned out like it did...
I am also including pictures from the inside, as promised. I would be terrible to mess that up...
Anyway, thanks for all your help, and sharing my agony!!!
I promise to come back with more questions