Chuck, ultimately it is just a centering ring, not the injector plate for an Apollo mission
A circle cutter attachment for a router [plus a router] and a 1/4 sheet of plywood and a ruler is all you actually 'need'. If one is patient enough, a hand saw and sandpaper would work but it takes longer. I have used the circle attachment many times for large centering rings that are dead on each time once the fixture is adjusted.
Getting a store to commit to a tight dimensional tolerance is asking a lot unless you tell them they can charge you for the scrap too, and even then they probably won't be happy about that. If you really want it CNC cut, then a serious cabinet shop would have a CNC router that does what you want, but you will have to pay for their time & overhead. Using the fixture you can theoretically hit a tighter tolerance and precision than the CNC cutter.
br/
Tony