I would look for something like a #0 wood screw with a 3" shaft. Or a similar machine screw. Important things are for the shaft diameter to be as small as possible, the thread end needs to be pointy, and the threads should be designed to cut, not fit into machined threads.

Then try to gently screw the screw into the hole in the tip, then pull. If that doesn’t work, possibly heat the tip of the screw with a lighter first so you can dig a bit deeper into the remaining plastic without causing it to swell too much. Then after giving plenty of cooling time, give it a pull.

There is a fair amount of friction to overcome if the tip is jammed at the end of a jack.

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