Headset cup removal problem

Hoping someone can offer some advice. I'm working on a late 80s Raleigh Montage, 88 I think. It has a u-brake on the rear which dates it.

Anyway I have it all stripped down, including the cup and cone bb.

The only thing I can't seem to remove are the headset cups, as the headtube is slightly flared on the inside top and bottom, so I can't get the tool to make contact with the edge of the cup.

What am I missing here? How do I get these out?