Optimising for Sum feels quite difficult, the solution space is very large.

I started with a tight-ish area solution with a high cycle count and kept reducing the interval between pulling inputs and checking the sum score. After 3 or 4 solutions I guessed the optimal would be around a 6/7 tape, but this 4.5 tape ended up much better. I did make a 4 tape solution, but I needed to double up on some of the deconstruction machinery which bumped up both the area and the cost significantly. Quite happy with how assembling the output came together, it felt quite area efficient. A nice change from the TracklessInstruction challenge!