Re: 5/8 gone
Just, if doing that, bees that have been queenless for that amount of time are more likely to reject the new queen (silly of them that may sound).
Their chances of a successful introduction will be greatly increased, if a comb of eggs and young unsealed larvae is given to them a day or two before introducing the queen, this will increase the successful introduction % greatly.
AND, another important thing, if the hive is left queenless 4 weeks, that will be about when laying workers start developing. So timing is everything get it requeened asap after last brood hatched.
And I guess the other obvious thing is after dequeening the hive, if the intention is to requeen with a caged queen, 7 to 9 days maiximum after the queen is removed have a good look through all brood combs which includes shaking off the bees, find and kill all queen cells. Leave it longer than that and some of them could hatch if the bees used older larve. They won't be the greatest queen but they can certainly mess up your attempts to introduce the one you buy.
44 years, been commercial, outfits up to 4000 hives, now 120 hives and 200 nucs as a hobby, selling bees. T (mostly).