With the rocket tool it becomes a one hit , quick job.

I own a pretty long flat bladed screwdriver I used it to tap on the inside edge
of the frame insert cup edge, reaching thru the head tube from the opposite end. tap, tap tap going around the edge.

originally bought the screwdriver to Pry back the wheel cylinders
on my old SAAB
to replace disc brake pads on it. leverage is Good.