Well, we discussed this a few times. A year ago more or less, the corks on my Cotter flute disintegrated, so there was no way i could even glue them back. At the time, with some encouragement from the people in the Woodenflute list, i replaced the dead cork with thread lappings.
Clive Catterall was one of the people who encouraged me to go this route, and he published some information:
http://www.flutes.fsbusiness.co.uk/tenon.html
At the time, other people (not Clive) told me horror stories about cork that is not fitted properly making flutes crack, etc. I’m not sure if this is true or not. Other people make it seem that replacing cork is very easy; you can buy a sheet of cork in a hobby store, glue it, and sand it down with sandpaper.
I guess if you search you could probably find some posts where i may have told people emphatically that they shouldn’t try making cork tenons at home, leave it to the pros.
Right now, i’m in a much more tollerant period. I can say that thread worked great for me; i have 2 flutes that have threaded tenons, and they work very well. I have no experience replacing cork. Can’t say much more than that.
I know a great repair store in this area: http://www.thebrassbow.com/ but i don’t know how good they are with wooden or antique instruments. They’re way up north for you, anyway, so may not be a good choice.
In your case, it sounds like the cork is still in good shape, and you just need to glue it. I don’t know what’s the best kind of glue, but i’m sure Loren and others do. I’m tempted to say “horn glue”. Elmer’s is probably good too. But i don’t know.
My personal, humble opinion, unless it’s just a simple glue job, send it back to Glenn.
g