Not sure how we got this far in without catching the fact that my calculation of total variance is wrong, but we did. Fortunately, it's the total variance formula that was missing a term, not the block sum variance (which would invalidate my theorem and pretty much send the whole paper back to square 1. Also fortunately is that the missing term was n/r, the total number of blocks divided by the number sampled. That converges to 1, so the asymptotic behavior doesn't change and the empirical results still stand.
So, bullet dodged and, as a bonus, having that term in there makes some optimality claims much more sustainable. I'll work on those tonight.
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