I have not used Goat Tuff glue, but have gotten inserts out using all kinds of other glue and epoxy with heat. Put in a field tip and heat that. You have to take care not to overdue it or get the flame on the carbon. I usually hear a little sound a see a little smoke when the glue lets loose. I then dunk it quick in water to cool down the shaft. I have not harmed a shaft yet that I can tell. If the drill bit doesn't work, give the heat a try.
I use hot melt for carbons. The only shaft I have had problems with are the GT's. For GT's I now just use a rat tail file to scuff up the inside real well, and then I clean it our with alcohol or acetone. I have not lost an insert from a GT since I started doing this. From time to time I may get an insert that will move out a little after a hard hit on something, but a little heat and it is back in.