Another way to tackle this: undo the nut on the top bolt, and carefully tape a long piece of thinnish rope end-to-end with the bolt. Pull the bolt through so you've got the rope running through the mast where the bolt used to be. You can now pull the downhaul system out of the mast, re-rig it, and when you come to reassemble simply pull the rope tight then slide the bolt back through.

Paul