OK, if you're willing to sacrifice the adapter, here's how to proceed.

1- hacksaw off the top as close to the headset as possible, so you're down to the 7/8" (22.2) section.
2- if necessary file off any remaining part of the larger diameter head.
3- remove headset, and drop the fork
4- now that the threads are exposed you can confirm if it's a French 25x1 or 25.4x24tpi thread.
5- if a larger adapter was forced in, the ONLY way you'll get it out is to file, ream or slot/cut it out. The method is the same as for frozen seatposts so a search there will help.

6- if it's not a French fork, then it's just bound in by corrosion, and you might be able to punch it out. Find a steel headset lock nut and thread it on until it's bottomed solidly. This is to protect the fork for what follows.
7- See if there's enough room to push the wedge down and rotate it 180°, so it touches high point to high point, and won't work as a wedge.
8- set the fork up over a pair of vise jaws with the locknut resting on top, and a gap for the stem to slide through. Use a solid punch through the bottom and drive the stem out pushing the wedge. (this method DOES NOT WORK if the wedge can't be turned around, because you'll just be tightening it. So you may still need to ream or file it out.