Years ago, Mike Kitner used a type of tubing to create these rings.
It was called "linen phenolic tubing".  It's stiff and easy to work with.
I think it comes in various sizes.  The size Mike used was 1-3/8-inch
outside diameter with a 1/8-inch wall thickness.

I used a radial arm saw to slice off the end of the tubing to make the
rings.  Later, after the pouch and ring have been glued in the valve,
I used a vertical mill to cut the two grooves in the ring for air
access, being careful not to go the whole way through the ring.

The company which sold the tubing was A.I.N. Plastics.  I don't know if
it's still available.  It was sold by the foot.  They have a web site.

Bill Black