It is out!
To remind: For years, my Warwick had a broken screw without me knowing. The head of the screw was glued into the hole to cover up before I bought it.
It took quite some effort to take it out. I took it to my uncle who has a workshop full of tools. First, we followed the collective TB wisdom and heated the thing up with a soldering iron. It turned out that the screw was too thin for the type of locking pliers at hand. So we tried a bench vice without success. At some point, half of the screw length sticking out of the wood broke off.
Plan B involved a small steel plate and a welding machine. We drilled a screw-size hole into the plate and welded the screw top into the hole. Then the whole construction turned.
The heat of the weld left a burning mark around the screw hole, as you can see in the photo above. However it has not burned deeply into the wood and not at all into the screw hole. After I took the photo above, I lightly sanded the area with a fine (400 grid) sandpaper and the bare wood appeared almost immediately, although still a bit darker than the surrounding area.
Anyhow, the screw hole can serve its original purpose again, while the remaining darker area will disappear completely into the neck pocket. I am happy with the result. Thanks again for all tips.
Cheers, BassChap
P.S.: P Town, sorry to hear about your father. I hope this last period in his life is bearable for him. Take good care of yourself.