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I'm picturing what is in the diagram, which maybe I'm taking too literally. It appears as a stone roller that doesn't turn. Even if you used a good modern climbing rope that can lift an entire truck, and has an additional mantle over the core strands for protection, it wouldn't last a day if you were lifting a 200lb person, because all the force is focused on that one rubbing point and would wear the rope away.
Rope isn't designed for abrasion when you calculate its tension strength. If you calculate the rope strength necessary for lifting huge blocks, then you might as well double its thickness, if it has a rubbing point like in the diagram, and it will still fail after probably less than 20 uses.
Just saying. You can't cheat in the model. Gravity and friction gets you every time.