I wrote a quick g-code program for my CNC router and tried cutting
out some of the pouch rings from 1/8" thick Baltic Birch plywood.
The results are shown in the attached photos.  They take a little
sanding to clean off the burrs.

A 60-inch square of Baltic Birch plywood costs around $14 and, if
the holding fixture was refined to hold the smaller pieces down better,
a sheet should yield between 800 and 900 pouch rings.

I asked an associate with a 90-watt laser if he could run a few
samples.  He cuts all sorts of parts and pieces out of Baltic Birch
plywood and his laser can cut up to 3/8" thick material in one pass.
They would probably not need any sanding or cleanup other than a little
point at the starting and ending place on the outside of the ring.

Bill Klinger
Arkansas

 [   CNC router with 1/8" cutter
 [ http://www.mmdigest.com/Attachments/17/11/02/171102_123632_PB020402.JPG
 
 [   Rings from 1/8" birch plywood
 [ http://www.mmdigest.com/Attachments/17/11/02/171102_123632_PB020403.JPG
 
 [   Close-up of ring after modest sanding cleanup
 [ http://www.mmdigest.com/Attachments/17/11/02/171102_123632_PB020404.JPG