Re: Fall breeder queens
AstroBee for what you are trying to do, overwintering an II queen will have more to do with how the II was done and little to do with her genetics. If one can survive winter I doubt that would mean her progeny are likely to be any better than the ones that don't. After all, we are not even talking about the survival of the hive, just whether they attempted to supersede the queen.
To maximise the chances of her getting through, restrict her egg laying right from when you get her, and winter in the smallest possible hive your climate can bear, small hives supersede less easily than big ones. But it will still be a crap shoot whether or not she gets through.
Larger breeders generally will not use a breeder more than one season anyway, as using it the next year means there may well be inbreeding via mating with drones from her own progeny the year before. A commercial breeder will often be happy with just a few months use from an II breeder queen.
44 years, been commercial, outfits up to 4000 hives, now 120 hives and 200 nucs as a hobby, selling bees. T (mostly).