After installing (if that’s not too fancy a term) the horizontal thread spool adapter on the HQ Sixteen, I laser-cut an acrylic disk to keep thread cones centered on the other vertical spool pin:

It’s trivial: an 11 mm circle to clear the washer and a 55 mm circle to locate the cone.
However, I cut that disk with a 56 mm OD, because that’s what I measured on half a dozen cones. Come to find out at least some cone bases are juuust slightly oval and they latched onto that disk like they were gonna be best buddies forever.
Rather than cut another acrylic disk, I laser-cut a friction ring from a scrap of stamp-pad rubber and jammed the disk against the chuck with a live center:

A few minutes of sissy cuts made the disk nicely round and concentric with the inner hole, with a little file work knocking the edges off the rim.
Done!