Headset replacement continued:
Use punch and hammer inside the head tube to get one end of the headset started moving. Insert a washer/socket small enough to barely slip through the headset hole and sit on top of end you got to move. Use the hammer and punch on top of the washer to finish removing the headset part.
Insert a washer/socket through the end with the headset part removed. Insert the 7/8" dowel on top of the washer. Strike the dowel with the hammer until the other headset part is removed.