Nicely done! (See what I mean about pictures side-bumping the page-width if you don’t trim/compress them?
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(And nice when things work out so it looks like I know what I’m on about!
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OK, first, if the crown was so tightly wedged in, there is some risk of it splitting the head tube if that swells with moisture, so reduce the lapping (replace with fresh and grease it) so there’s just enough to keep it snugly in place in the tube-end, but you can twist it out with your fingers.
Nice touch by restorer, if 'twas s/he, to leave the original pads with the flute. Or perhaps s/he didn’t remove the crown and they were put there by a former user. The unused ones look as though they might still be serviceable!
As for making your new stopper, try this. Keep your cork whole. Measure the head bore at the crown end and mark a circle that size on the end of your cork. Use a very sharp blade to trim away some of the excess cork slicing down the sides from the marked ring. Then you’ll have to sand it. If you have a drill press, you can try mounting the cork onto a screw (centre of the end you didn’t mark) and mounting it in the drill chuck as a make-shift lathe, then use a strip of sandpaper against it as it spins. of course, if you have a lathe…
Otherwise, you’ll just have to sand it by hand - wrapping your sandpaper around a block of wood and rubbing the cork against it, turning frequently is probably the best way, but it is hard to keep it perfectly round and cylindrical! You may ruin a few corks before you get one good enough! By keeping the cork’s full length as you work you both make handling easier and have more of a chance of getting part of it’s length to the right dimensions, and you can keep checking it against the head tube crown opening. Aim for a snug but not excessively tight fit. When you’ve succeeded, cut it off straight across at one end (assuming the original face isn’t usable), measure a piece about 2cm long and cut off the other end. Fine-tune the sanding, sand the faces flat if necessary, grease it up and pop it in!
Use your dowel to push the new cork in until you can see it looking through the embouchure, then mark your dowel at one end with the head bore diameter and put it back in from the body end and push the cork back until the marker line is in the centre of the embouchure or a little towards the crown end. Suck test the head, then try a toot!