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Josh's graph with (only?) 1500 datapoints suggests otherwise.

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Actually it doesn't suggest otherwise. It just doesn't suggest anything. If you look closely at the BB/100 graph you will see that it is much too granular to draw any sort of conclusion on convergence properties (how closely it approximates normal). There are only 38 different points on the x-axis each of which have having frequency values between 0 and 11. To even have a shot at drawing a reasonable conclusion we would need something more like the BB/10 granularity at the BB/100 level. This would require a 1.5 million hand DB instead of a 150k hand DB.

I do agree with you, however, that this is interesting and is worth looking into. And I think that Josh's method (looking at empirical data) is the best way to do it because we don't have an accurate theoretical model for a hold'em probability distribution.