I’m sure Robert Bigio would turn you a conventional 8-keyer’s straight-sided/flat topped (with face-decorative turning) crown for one of his gadgets if you asked him! http://www.bigio.com/stoppersandcrowns.html
I’m sure Casey will correct me if I’m wrong, but I seem to recall that my folk flute has a (turned? standard size?) wooden dowel wrapped in thread. However the flute is out on loan at the moment, so I can’t check. Seems to work fine.
I didn’t know anyone else did this! I do the same thing, using synthetic corks, but don’t do the heating part. I just twist it back and forth, slicing down into the cork, until I reach the desired size. I think your way (Jem) is better, but I’d be worried about the “heat” part. One thing you can guarantee is that the cork WILL be the right size!