Hi, I often rig up my Tornado and go out solo, and the technique I use to rig is to take my righting line (tied to the mast base), string it out in front of the starboard forestay attachment and around under the hull, take it across to the port hull and wrap it around the hull aft of the forestay there, then make a loop in the rope in the center of the hulls and string the end through the loop, then I tie up to a dock. (I hope this makes sense).
I find that when tied off in this manner the boat stays head to wind regardless of shifts, gusts or waves. If you left the loop in the righting line in the right place permanently, it wouldn't be too hard to do this on the water, although maybe not to easy either now that I think about it. Then you could furl the jib (or detach it from the sheet), release the clew of the main from the outhaul attachment point and tie off to the other boat's stern.(and pop up the rudders) Your boat wouldn't sail anywhere and you would be attached by your righting line.

If you simply tie up with the righting line attached to the mast base, the boat sails all over the place.

My only other thought, if the lake is that small, why not just drift to shore and then self-rescue in shallow water?

I'm with everyone else, don't leave your boat (unless you've tied them together).
Think of us northerners during the long winter.
Al