Have you tried removing the stem so you have better access to the wedge? Often if you do that you can screw the bolt in and pull the wedge out, then reassemble it away from the bike.
The other approach is to again lift the stem out, remove the front wheel, then turn the bike over and push the wedge out from the fork side. If you have a front mudguard you will need to remove that too, but almost always the bottom of the steerer tube is open so you can get the stem bolt or another long, thin object against the wedge and push it out that way. You may need to hammer it a bit, so preferably use a long punch or spare bolt, rather than the stem bolt that you need to make it all work.