"This can happen if the queen is mated with a closely related drone."
A queen has two different sex alleles. A drone only has one so 100% of his sperm carry the exact same sex allele (barring a mutation during gamete development). If the allele in the sperm is the same as one of the queens alleles and if she only mated with one drone then 50% of her eggs would be diploid drones and 50% ordinary workers. This does not appear to be what the original poster is seeing. He sees no larva at all. So, I see zero evidence that inbreeding or diploid drones are any part of his problem.
Dick
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