insert a small length of 1" metal tubing in the head tube until it rests on the upper rivet and tap gently......you'll find the rivets pop undone this way quite easily
Drill them out slowly with a dremel. Finding the right size rivets to replace and a rivet gun that fits is near impossible though. Best finish is to cut the head off an old spoke and glue it in place.
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We had rivets that were a mushroom on one end and straight at the other, we had to form the other mushroom by hand using a rivet former.......blooming nightmare.
For my Flyer I used copper dome head rivets and filed the stems protruding inside the head tube to make a burr which held the rivet and headbadge in place.