A tripping line for a JSD would be good, but if deployed with the drogue, it might twist around it and close the cones and no longer work as a tripping line.
So how about deploying a tripping line when you want to bring the drogue back on board? How? - The same way as with a stuck anchor. A loop of chain on the end of a long rope with a small parachute drogue (or bucket or maybe a fender) attached to the loop. The idea being to let the boat's forward motion carry the bucket and the chain loop back down the JSD until it reaches the end. Ooops! A grappling iron needs to be on the end of the JSD to catch the chain loop. When it does, haul in the tripping line.
Might it work? Or would it simply snare on the cones? Maybe a ring or funnel would be better at reaching the end sooner than a chain loop.