atmo,
Something that may work well for you is a fixture similar to what McMaster Carr calls a "Shim Stock Punch Set". Basically its a punch and die fixture doweled together with a space inbetween so that you can insert the shim stock to punch holes. The upper plate guides and aligns the punches with the die and you just use a hammer to punch out the slugs.
From my die making days I found that it is easiest to punch out the inner diameter first and then punch the outer diameter. If the punch is made with a small hole in the center of the cutting surface, you can make interchangeable pilots that register in the hole and are stepped to the diameter of your shim ID's so that you can perfectly align the inner and outer diameter. A good toolmaker could fabricate something like this for you in about a day.
Hope this helps!!!