Sam, I think you are confused with the drawing. The bungi is NOT used in the system, it is there just store it all when NOT in use.

Let me try to explain.
Trap wire comes from the top section of the mast.
Connects to a shackle
Cleat (NOT a cam cleat) connects to the shackle.
Bungi cord can be connected to the same shackle as above.
2:1 purchase line goes through cleat.
same purchase line goes down to a small single block attached to the handle, or in Wouters case goes through the dog bone, back up to the cleat.
Line goes through cleat, and the bitter end will have the stopper ball, so you can pull on it, or so you do not go splash.

According to a few folks here, it will work. I am confident enough it will work.