I myself prefer the extractor method. Use a left hand twist bit and many times it will come out when the pressure is lessened by the hole. If not, I use a set of snap-on extractors that I bought as a set with the left handed bits. I can't tell if the threaded portion passes all the way through the back of the mount from the picture, but it would be much easier if it does. Use cutting fluid and take your time to get the hole drilled straight through and you should have no problems. I also recommend chasing the threads with a tap when you do get it out.