> I have it in my mind that the queen, being diploid, will have a re-shuffled assortment of genes in every egg that she produces, the same as with humans, and so each drone will be different.  On the other hand, the drone, being haploid, will produce identical sperm.  Or am I confused?

No, I was the one who muddied it up. We always hear that the drone has no father, receiving only genetic material from his mum. However, as you say, the queen has genetic material from both parents, and this material is shuffled when she produces eggs (meiotic recombination). The drones produced from said eggs will be different. But the sperm they produce can only have the maternal contribution since they are unfertilized (no daddy). 

> Haploid drone bees produce haploid sperm in their testes through a mitotic spermatogenesis without a meiotic reduction division. http://waynesword.palomar.edu/lmexer2a.htm

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