Another way, would be to make the same spindle register (fitted to and centred on your rotary table) as is used on your lathe.
This way, you turn something on the lathe, remove the chuck with workpiece still chucked and move the chuck to the rotary table for the second op.
If necessary you can still take it back to the lathe for further turning.
This is easier with spindles that permit easy chuck removal ie short taper noses, rather than the usual threaded spindle nose.
I know that this doesn't solve your immediate problem, but perhaps for the next time?