This reminds me of a command "parent -s -r". It does the same thing as our usually parent command. Its just that in MAYA in order to reparent shape node under another transform node, we need to "type" in command. The usually drag and drop in outliner or hitting p won't work.
So the same thing, choose the child(ore children) then the parent (remember to freeze scale first...), then run the command "parent -s -r". This way we don't need to parent the curves under the disc ctrl, then make them reference. Save some time!