Paul is there any chance you could turn a disc from some layers of MDF sized large enough to create a cavity into which you could jam fit your wheel. What I am trying to describe is a three layer MDF jig. Two layers are discs glue solidly together. The third layer is a circle of MDF layers thick enough to accommodate your wheel glued to the face of the two layers glued together. This whole contraption should be mounted on a face plate and trued up on the outside diameter. Then the internal diameter of the circles should be carefully sized so that the wheel can be jammed inside and held securely.
I cannot tell if you have sufficient clearance around your disc for the disc to swing freely and not hit the lathe ways. If you could do that and apply a little tape to the outside edge of the wheel overlapping the MDF and a screw or two to the center of the wheel blank disc neither would go anywhere when you parted them. I would make a wide parting cut working it down gradually so there is no chance of binding when you finally cut through the wheel blank.
Since you are making multiple wheels the jig could be used over and over. A hole or two around the inside of the MDF circles would allow you to tap the jam fit wheel out from the back side.
I doubt any of this makes sense.....Maybe someone can do a better job of explaining it.