Hi buddy, how about using a sacrificial cork sanding block cut down to fit the shape in the middle of your headstock so that when drilling the bit can go through into something to prevent tearing out?

I know it is really slow and painful but another way is to just run your power drill in reverse and be patient. Pushing it in reverse just makes things hotter and could end up burning or scorching the timber. This is how I enlarge any holes on bodies to accommodate thicker diameter upgraded pot shafts.