Do you need a box / basket? I`we been thinking of making a "bag", bottom same size & shape as the trailer. Some sort of system to attach in all corners. Make it taller than you need. Roll it down in the top the way some waterproof bags are rolled. Welcro or similar to secure in the top. That way you are free to put big / long items also without remowing the box.

On my homemade flatbed trailer I use a wire (steel) basket made for storing chlotes in a wardrobe. You should be able to find bigger ones if you look around. Mine is approx 96x58x25 cm`s. I am going to combine it with a bag like described above.