One of my HEs wants its ring gaskets to remain on the head. I can't get either to budge. Any ideas?

hit it with a torch? dry ice? not sure which would work best.

I have successfully used a flat blade screwdriver between the copper gasket and the head, twisting the blade to cause the ring to collapse. You do have to be careful not to damage the land that the gasket seals to, otherwise it is a prime candidate to leak later.

Sometimes these are swelled in a way that they are difficult to remove. I used a small drill like 1/16" and drilled into the long side. Be careful not to deep and go into the head. I then used a tool I made that had a 1/16" pin at the end. A snap ring tool may work. Use this to pry the ring towards the center. This will deform the ring. It will either fall out or at least give an edge that you can grab to pull it out.

I use the same method as Dave P

Bent screwdriver

or

Seal pick

The problem is getting leverage or getting a hold on it.
I made a tool using a coat hanger.
Simple, Cheap and works for me.

--- bill
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I had success with a bent pick. $10 at NAPA.