Go to the hardware store and find a washer who's OD approximates the ID of the head tube.

File 2 flats to make it as racetrack oval. Now you can slip it past the head cup where it can flop over to span the inner lips. That will allow you to drive the cup out using any solid punch.

OR you might use dental floss wrapped around the tines of your tool to hold them in the retracted condition. Slip it home, then use a paring knife to cut th we floss and allow to spring open.