Spay Plusgas and leave for a while.
If the cup removal tool jumps of the cups then get the forks (or an old spare set) and push the steerer into the cup removal tool to keep it engaged. This will hold the tool and stop it skipping of the cups. Then hit the tool with a large hammer. I guarantee it will budge eventually. A good quality stand built entirley of steel helps here.
The screwdiver method will probably work but the above method is quicker if you have the right tools.