You'd need to use even pressure around the entire ring simultaneously to avoid damaging the ring. In other words you need to press it off. You might try a pulley-pulling tool, it uses two semi-circular pieces with a lip that goes under the edge you're lifting, and a collar to keep it together as force is applied. It's a shot in the dark though...
When I did mine I used flat edged hand tools and a small piece of wood for a fulcrum; when you get one side to move up a little, you have to keep working around the outside so you don't press one side too far making the opposite side harder to budge... it's almost just worth getting the new tone rings. How often are you gonna have that apart? Might as well do it right while you're at it!
"I'm gonna sing the doom song..."