If it was me - and I am glad it is not - I would go with a larger and larger bolt extractor. At some point I would expect that it would work.
We're talking EZ outs, right? They look like this:
Eventually, of course, you are going to have to get the piece out. Do whatever it takes, and then you are going to have to re-thread the hole. That will be done one of two ways:
First you may get the job done by using a thread chaser of the correct size. You'll want to do this if the piece comes out and you decide the problem was that you cross-threaded the plug the last time you put it in.
If the threads are ruined and in too bad shape to be re-tapped with a thread chaser, I would go with a HeliCoil and install new threads. Helicoils look like this:
They come with complete instructions and will give you a permanent fix. Basically you will be drilling out the hole, retapping it to accept the Helicoil, and installing your plug into the new Helicoil.
Also: Keep your eye peeled for a plug that is only SLIGHTLY larger than you old one. That way you can just. re-thread to accept the new plug.