The old trick to remove the "fixed" cup is to clamp the thing in a vise, and use the frame itself as a wrench.
Liquid Wrench is good stuff; a bit of judicious tapping with a hammer makes it penetrate better.
I too have used drift-punches, chisels, screwdrivers, etc., all whacked with a hammer. If it gets too bunged up, any decent bike shop should have a few lying around in the old parts bin.