If you can find someone with an induction heat tool, that may work. I would cut a slot in the broken part, heat with the tool and stop before the surrounding material became too soft, just enough to break free and back out with screwdriver.

I bought one off Amazon last year and have used it countless time when usually all hope was lost in getting a bolt out in a tight spot. Just used on someone's license plate screws that were seized (machine screws in a captive nut on the hatch).

I have a knock off amazon one, was cheaper when I bought it. Amazon Inductor Tool