If your ever faced with a similar situation you might give the following a try,
Tools required,
fine point soldering iron,
plenty of patients
can of Kroil
I have used this procedure on countless small screws and other threaded joint over the past 30 years or so working as a millwright and fiddling with guns. It has taken as long as two days but is usually over in a matter of hours at the most.
Take the soldering iron and warm up the screw, nut, or item. Not hot sa you can get it but simply warm to the touch. Then add a drop or two of Kroil, and let sit for 3-5 minutes. Then heat the item up again until you can just see the Kroil start to boil or smoke or until you feel it's all the soldering iron will do, then add another drop or two of Kroil. This will usually expand the threads a little the first time and allow the Kroil to penetrate down along them. The second warming will do the same but this time it also helps to break up the rust particles between the threads. The additional Kroil will help to move some of the crud out of them as it passes down and around them.
At this point apply a bit of pressure to try and remove or if this fails tap on the handle of the driver being used while it's on top of the screw to help break up the gunk. Repeat as needed.
Usually this works on even the most stubborn situations. I have used the same procedure to a greater extent to remove nuts from bolts that you could not even tell there were threads on due to the corrosion. Kroil is one of, if not the best penetrating oils out there for breaking up stuck threads. Give it a chance to work and be patient and you are usually rewarded.
Hope this helps someone.