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The next piece of (ma)bati I sighted in the kitchen was an old cookie box - for some ppl that's just rubbish but for me it equals a source of clean, thin sheet metal that I could use for the repair.
I cut out the desired size, double-layered it (to improve stability)....
...and used flat pliers to mold it around the remaining parts of the hinge.
After some small adjustments, the "new" hinge just fit in perfectly well:
I write books. My latest is a YA science fiction novel called Homeland (it's the sequel to Little Brother). More books: Rapture of the Nerds (a novel, with Charlie Stross); With a Little Help (short stories); and The Great Big Beautiful Tomorrow (novella and nonfic). I speak all over the place and I tweet and tumble, too.