Milking maids, or their 3 legged stools, are barred from my shop! (says he sheepishly)
But to be serious for a few seconds.
My oriental lathe with screw fitted chucks uses two clamps fixed to the back of the chuck to hook behind a chamfered flange on the mandrel, to prevent the chuck going AWOL when running in reverse..
Suggestion for the brave and innovative.
IF you could make up a split ring, with a chamfer on the back face, and clamp it to the plain dia behind the register, maybe a couple of "hooks" could be attached to the back of the chuck, to prevent the chuck unscrewing on the odd occasions when you run in reverse.
Drill/tap two largish dia shouldered "studs" into the backplate, on a diameter, and tap the outer end of the shoulder, radially, to take the screw fixing the "hooks"?
When I had a ML7, it lacked this feature, but by GENTLY tightening the belt, and taking light cuts, (never tried screwcutting – where the cuts are likely to be heavier) it was possible to run in reverse without the chuck coming loose. Maybe I was just lucky.
Howard