Have you tried a weeny bit of oil on the screws when you put them in?
I have used a core cutter to remove screws like that before then cored a new bit of wood to glue back in the hole.
Let it dry then cut off any protruding wood, drill new holes and fit the hinges.
Like a hole saw?
Anyway I got lucky, two did come out.
And I was stuck, as I didn't know what to do, so unusual.
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They would have been very useful. I'm done with woodwork for a bit, but now that I know they exist......Titanium Plug Cutter Set
Create precisely-sized wooden plugs or dowels to fill counterbored holes in wood. Titanium-coated for an extended life, Toolpak's plug cutter set includes 6mm, 8mm, 13mm and 16mm sizes - perfect for hiding sunken screws.• 55mm plug cutters in four sizes - 6mm, 8mm, 13mm and 16mm• Makes precise...www.toolstation.com
This is what I have used in the past, put over the offending screw and core round it, break the core off with the screw in it.
Then use another core to fill the hole.
Glad to see you had some success! Those Knipex slip joint pliers are awesome, i've had some luck with them before too!
That is looking superb by the way!!