My ducks have not used small boxes to lay eggs. They just go in their big box and lay them in the wood shavings. I am curious what your little boxes look like?
I am amazed at how different duck habits are compared to chickens. I am glad I didn't house them together. The chickens go to bed at a decent hour. My ducks just take little cat naps, and party at night in their tub! They would keep the chickens up if they were together!!!
For my duck boxes I got old large tupperware storage totes with lids. Then cut an opening out of one side. Stuffed with straw and put out for ducks to try out. I'll try to take some photos. My ducks stay up all night too. They have duck parties at 2 am, forage at 6 am, and nap at noon. I wish I was diurnal too!