The plastic tips can be replaced of course (pack of 4 tips at a cost of 15% of a new Pencil!), but there was still a broken portion inside the Pencil that would prevent a new one from fitting. As the tips just screw in, I was able to get some purchase on the fragment (below) with a sharp pin and slowly unscrew it (remember: righty tighty, lefty loosey). It took a minute or two, but then it was out and I was able to fit a new tip. Everything works again!
Well done sir.➵