It turns out that the outer diameter of CD platters isn’t quite as perfectly controlled as you (well, I) might imagine, although the differences between CDs from different sources amounts to perhaps ±0.1 mm. Of course, instantly after putting the tape-down fixture into use, the next few discs atop my stack of scrap CDs were just large enough to not quite fit.
The Sherline’s workspace can’t maneuver the holder’s perimeter around the spindle, so embiggening the OD calls for the rotary table. The general idea is to clamp the center of the fixture to the rotary table, run a small end mill about 0.1 mm into the fixture’s OD, spin the table one revolution, and be done with it.
Of course, the rotary table’s 3/8-16 threaded center hole doesn’t match the fixture’s 6 mm center hole: we need an adapter. Start with a 1 inch long 3/8-16 stainless steel hex bolt, center drill the end, peel off the hex head, then turn to 6 mm OD, going down far enough so the threads don’t stick up out of the table too much:
The Sherline uses 10-32 screws, so poke a #16 drill 15 mm into the bolt to get maybe 25% thread depth (because it’s a blind hole into stainless steel for an application requiring minimal strength and I hate breaking taps), tap 10-32, clean out the hole, and call it All Good:
Find the trim plate from an old faucet to reach around the central boss, stack up enough flat washers to meet the nut, snug a Sherline spherical nut + washer set (because it’s within reach), chuck up a 1/8 inch mill, and have at it:
The fixture sits atop an aluminum plate cut to fit a smaller version of the table riser, but this requires zero fancy alignment. The 6 mm adapter centers the fixture on the rotary table and the cutter sits at a fixed radius from the center wherever it contacts the fixture rim; just spin the table and it cuts a neatly centered circle.
A test fit showed the oversize discs fit perfectly:
Bonus: a nice new adapter for the rotary table!