You can remove the broken extractor using an annodize process. Take the valve completely apart so that only the section with the broken piece is remaining. Mix up a 3:1 ratio of battery acid to water and put it in a plastic tray. Put a piece of aluminum inside the tray on the bottom. This piece of aluminum has to have an aluminum wire running out of the solution. If you have a plastic grate to sit on the aluminum on the bottom of the tray, it would be great. Connect a +12V computer power supply line to the valve section using aluminum wire or rod. Make sure there is a good electrical connection or it won't work. An aluminum rod threaded into the valve at the field strip screw hole might be the way to go. Run a tap in first so that any annodize in the threads is removed. Put the valve into the solution so that it is completely covered. Connect the 12 negative lead to the wire/rod connected to the aluminum on the bottom of the tray. Turn on the power supply and watch the bubbles coming from the ferrous metals. You might have to make waves near the bubble area to allow the bubbles to release from the metal which will allow new acid to come in contact with the area. After a few minutes, the ferrous metals will be totally dissolved.
Except for the Automag in front, its usually the man behind the equipment that counts.