broken heel advice ...

[Arnold Schnitzer]

You need to patiently work a sharp seam-opening knife into the seams until it all comes loose. Dripping in a little grain alcohol may help. If the glue is really tough, heating the knife may be necessary. (You might want to be careful using a hot knife around alcohol.) You could also try injecting steam if all else fails. If none of this works, chisel out the remaining piece bit by bit, and then clean out all the glue, and any wood/glue left on the button. Then you can make a new piece to add onto the neck.