"I'm not ignoring the probability of genetics playing a big role.
Do you know if the Q uses up the sperm of one male at a time (maybe last-in-first-out?) Or if she is selective? Or maybe it's random?"
genetics does, both the queen's genetics and drones she mates with.
your question on the sperm stored.........this is a great question. i do not know the answer to this question. i am not a scientist,entomologist or queen breeder.
having said that, it is my understanding from reading/studying on queen breeding/rearing that it is mixed. sperm goes into the queen's oviduct then to her spermatheca where it is stored for her lifetime. (the queen mates, sperm is mixed in her oviduct from the drones she mates with, goes to her spermatheca). also my understanding that a queen only stores about 1/2 of each drones sperm she mates with. so from my understanding, not one drones sperm at a time, not last in first out, selective or random, but mixed.