Here is a thought.
If you have access to a lathe you could try using a piece of round stock chucked in the three jaw chuck, then another piece that is center drilled but fairly thin on the end of a live center in the tail stock. Both of these should be smaller than the finished size of the disk.
You might try and use some very fine sand paper, maybe 240 grit rubber cemented to face of each of these. Then put the disk in between, center with a dial indicator or you can even do it with something held in the tool holder like the tool bit you will use to cut them, depending on the tolerances you need. Then take real light cuts.
Lemme know how it works out.
DonT