SWM: Well, yes (as he lifts his head sheepishly to reply), I do respond on some topics in a rantish fashion. Michael Faraday was not a college-schooled, certificated person, but a well-reasoned, astute observer. While having the first half of that, I occasionally muster the skill to be the second. I make mistakes, too. But no one should take the word of a certificated person when it runs counter to his own eyes. Yes, your eyes may fool you, but then you're not observing carefully enough. We should just keep at it and remember our limitations.
Seems we are in basic agreement. Look at the development history of Walt Wright's "Nectar Management" for some hints he provides on this topic of post-solstice queens. Walt's observations included that his queens laid like anything into the open brood space he provided through his checkerboarding, in his time and place, with his bees. Then they were superseded for reasons he didn't determine. His observation was that it routinely happened. Some others who corresponded with him did not see the same things with their bees, at least not as a uniform pattern. But Walt's observations dovetail with Disselkoen's observations about post-solstice queens being a Good Thing To Overwinter. Disselkoen makes what appear to be speculative words about day-length sensitivity, concerning the validity of which I have no idea whatsoever. But both of these astute observers found that later-summer queens were beneficial. Neither concluded confidently why this should be so.
Disselkoen credits Miller with noting and publishing the tendency of worker bees to turn cut cells into queens at the bottom of chevron-trimmed comb. Miller, in Disselkoen's view, didn't recognize that simply turning a cell into a downward facing cup seemed to be the crucial trigger. Hopkins found this in his "turn comb horizontal" method of making queen cells, but Disselkoen uses both in a simple fashion to guide and suggest to the bees where to place queen cells. The bees don't always listen, but there is a bias in their response.
It would be useful to understand why post solstice queens did well in these two areas. I find it uncompelling that the bees simply out-reproduce the mites. There is always a population reduction in bees, and the mites don't automatically die off as the bee population decreases. Now, if the queen rears the winter bee population with fewer brood cycles, that also cuts off some of the growth cycles of the mites, and could reduce the mite infestation proportion. But (as you said of yourself) I don't know.