John I think you could add a bungee before the cleat.

Scott-
A bungee/shock cord section could possibly work, as you and Bill have suggested. One of the commenters at the MEC site (yakadoozer) also suggested the same thing.
A shock cord section works well in the older style 2-line rudders where a cord retracts the rudder and deploys it. Usually the cord is above deck and looped through a padeye near the cockpit - you pull on one side to retract, on the other to deploy. I've seen arrangements with a knot or a plastic bead on the line to give an indication of the rudder position. In those setups there's lots of exposed line, so plenty of spots for inserting a shock cord section. The same setup can be used for a 2-line skeg control.
Once my friend brings the boat around, I'll have a good look at it.
My recollection is that the control line (downhaul) emerges from the deck right at the jam cleat, so there's no space for inserting shock cord there. At the stern there's more exposed line, but not a lot, so there may be possibilities there. Another consideration is that there is a LOT of tension in the downhaul line when the rudder is deployed. Remember that there needs to be enough tension in the coil spring to flip the rudder blade 270º up on to the deck. So the shock cord will need to be quite hefty to keep the rudder in the water, and might not be able to allow the rudder to move over kelp, though it might be able to prevent breaking the foil if a rock or log was hit.

I'll try to get some pictures when I get to see the boat again.