This approach was the best I could find, but I'm not convinced by it.  It doesn't quite have that Summy feeling.

On the other hand, this puzzle inherently challenges Sum.  The minimal in-out ratio is 10:1, so even at Period 4 we're looking at a floor of ~250 cycles. if we're aiming for the typical sweet spot of G~=C, that's quite a large budget for mechanisms.

Moreover, the 10:1 recipe is much harder to manage than this 12:1 throwing away tin and lead. At this ratio, the C floor is closer to 300, suggesting a Sum target around 600.  That's 50 better than I found...and would still be the highest Sum record on the leaderboard.  Yes, the puzzle is hard, but I'm not ready to believe that it is this sort of unicorn.

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In my defense, all this theorycrafting is ex post facto.  My initial approach resisted the high-G budget, and attempted a cheap P6.  But at 150 cycles slower than P4, there was no way to save enough G on mechanisms to justify the relaxed cadence.  

I also tried a machine that was aggressive about cycles, operating at mostly P3.  But the waste handling at that speed required enough cost and/or space to just overset the C savings.  So P4 does seem to be the best balance, which brings us back to that ever-so-unsavory target of 600 Sum.

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I don't know.  Perhaps a different recipe would do better?  