I had some Greek ( Crapolian??) bees at one time... queens were big and wide and easy to find even bigger than the drones..... perhaps cross in some Greek genes into the mix..... a Zorbfast?
They were not very fecund ... ate all their stores, so I did not get a honey harvest from them. Died out when I foolishly opened up the colonies on the coldest day of Winter to pour the horrible syrupy acid over them... dead by Spring with Nosema!
Perhaps not suited to the Devon temperate maritime climate...... that was in the days before I moves West across the Tamar!
Yeghes da
Cecropia. Had much the same result several years ago...and no acid involved. Queens were nothing extraordinary for size, but gee they were slow in spring, got very much less honey than my preferred strains, and most died first winter. Very few survived a second season.
Other types (apparently) from the same area fared even worse.
Not a uniform tale however, as some beekeepers really like the Greek product.
Large queens as such are merely a general indication of a queens nutritional status during development and thus her potential to be good. Its not in any way a hard and fast call, as many large queens are not especially vigorous layers, and some remarkably small ones perform brilliantly.
We have one amusing example right now in our own unit. Jolanta was harvesting queens in the mating apiary one day and was gnashing her teeth at one Apidea, as a queen was laying a lovely pattern in it yet she could not find her. Eventually we did find her, and she was actually marginally smaller than a worker and very hard to see. She did not have the heart to administer the crunch treatment so caged her up anyway. Later that day we were introducing queens into splits and came up one short.....all that was left was the tiny queen, by now nicknamed 'mini'. Well we gave it a chance in the sure knowledge it would supercede. It didn't. During a couple of visits to the bees on the heather by associations (we do a couple of these every year) the challenge was for some of their members to find the queen 'in that hive over there'...... only one ever found her.
Yet she performed just as well as the other queens in the group, has overwintered in fine condition, and is sitting on an OSR field just coming into flower with 8 bars of brood and has been supered. Yes. 'mini' is still going strong. Strange. Goes against all I expected to happen.