> but it is the length of time the "royal worm" (I love that term) eats "bee milk" that makes the diet so much more protein rich than that of a worker. 

That may have been thought of as correct at one time, but not any more. There are specific substances that induce queen characteristics, so it is not about quantity, nor duration. 

QUOTED MATERIAL:

The honeybee (Apis mellifera) forms two female castes: the queen and the worker. This dimorphism depends not on
genetic differences, but on ingestion of royal jelly, although the mechanism through which royal jelly regulates caste
differentiation has long remained unknown. Here I show that a 57-kDa protein in royal jelly, previously designated as
royalactin, induces the differentiation of honeybee larvae into queens. Royalactin increased body size and ovary
development and shortened developmental time in honeybees. Surprisingly, it also showed similar effects in the
fruitfly (Drosophila melanogaster).  

These findings indicate that a specific factor in royal jelly, royalactin, drives queen development through an Egfr-mediated
signalling pathway.

Royalactin induces queen differentiation in honeybees
Masaki Kamakura
Nature 473, 478–483 (26 May 2011)

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