Unsurprisingly, the mini-lathe lacks enough stiffness to apply enough force to hold a disk in place while turning its rim:
The old South Bend lathe had mojo, but those days are gone.
So drill and tap that fixture for an M3 screw, then stick some coarse sandpaper to it:
Snug the screw (a Torx T9 from the Small Drawer o’ Random M3 Screws) down on a rough-cut disk:
Sissy cuts remain the order of the day, but the screw applies plenty of clamping force and doesn’t require the hulking live center.
The Smell of Molten Projects in the Morning 