In the past I have used a set of vice grips and did the pull and twist method.
If that does not work, I have also grabbed the head with the Vice Grips and used a block of wood against the case and pried against the wood and the Vice Grips.
When that fails I have used a bearing splitter or I drill it out.
The idea of drilling the plug threads with air blowing in from above is good.
Another thing you can do is put a good amount of grease on the drill bit to help catch the shavings and prevent them getting loose in your case.
After the plug threads have been repaired, I like to flush it out with some ATF or diesel.