anti sieze will not "burn off". Use the copper one.
As far as getting these out, drilling is only a last resort - because it takes so damn long. If you snap the heads off of the bolts - fine. the axle backs will come right off. Then you can try
1. Vice grips - with the axle back off, often this removes enough pressure making vice grip removal possible.
2. Weld a bolt onto the broken one. the heat will help loosen the threads, and you will have a new bolt to unscrew.
3. Only if 1 and 2 fail - drill away. Most aftermarket axlebacks do not even use a threadded flange, so do not even worry about re-tapping. Just put a nut on it (that's what she said

)