Tim,
I have been trying to use a thickness planer to take 6" wide sheets down to 1/16" or less. The planer only goes down to maybe 3/32 so I have to use a second board to pad it a little, but with poplar when it gets that thin the blades lift the wood and chew it up rather than cut it smoothly and it's a mess. So I'm thinking a drum sander might allow us to grind off a little more material. The planer gives a decent enough finish so that can still be the visible side and it probably doesn't matter what grit the other side is finished with if it can get us a little thinner, but taking it down to something "smooth" would be nice. I can plane a couple of sheets and bring them to the space if you'd be willing to see what more you can do with them.
The thinner we can go the smaller I think we might be able to make something like this picture (more jewerly-scale stuff - this piece is just under 1" OD so a little big for earrings).
Thanks,
Bob.