Yes, this is the correct interpretation of my question, and thanks for your suggestions. I benchmarked your two suggestions relative to my original, and things are definitely improved: 
            Rate      orig substring  blokhead  blokchop
orig      1199/s        --      -45%      -62%      -69%
substring 2162/s       80%        --      -31%      -44%
blokhead  3144/s      162%       45%        --      -18%
blokchop  3840/s      220%       78%       22%        --

[download]
"Substring" is closer to my original (too verbose) style, so some of the gains are also coming from the more succinct, easier to read code. Best so far is the "chop" based suggestion.

Still wondering if there might be other improvements, or some vastly different way to solve this.

Thanks for these suggestions, they really have helped.
-a

In reply to Re^2: Speeding permutation counting by albert
in thread Speeding permutation counting by albert

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