I have nothing against dark tiger striped queens other than the amount of propolis that they deposit all over the hive. they winter will and do not eat themselves to death. what i was implying is the genetic make up of the queen can have a huge impact on how the colony preforms and their temperament. In the seventies and eighties the bee most were raising was the big fat gold colored Italians. the built up large colonies Produces a lot of honey and as long as they had enough food to keep from starving to death they would keep producing brood. The finest best producers were selected each year to produce queens for the next year. This selection process was repeated year after year for the previous 50+ years. Some hives overwintered in northern areas were winter dead outs because of starvation but a 2lb replacement package could be bought for $18 dollars. To buy a queen by herself was $8 dollars, so a lot never even tried to over winter. 1987 and the first of the mites appeared in north America and over the next 5+ years the previous 50 years of breeder stock selection was wiped out. They went from breeding from the best, to breading from what had survived. In the early 80 the queens all preformed close to the same. Now there can be such a shift between colonies in temperament, color , characteristics, and production.
Now more emphasis is put on colony survival, But if it is going to survive, but produce no surplus of a honey crop to reward the beekeeper for looking after them and seeing to their needs, Is that genetics worth having? If they are only providing pollination for your garden you may as well put up mason bee blokes and bumble bee boxes.
Sorry got on a little bit of a rant here
If bees wont build up into the top added supers, then you may have to treat them as a beekeeper keeping Warre hives would and bottom super. The bees will keep storing the nectar and keep forcing the queen down. and as the run out of space to store the nectar they will build and draw comb for the queen to lay in
