I think this full box trading is more focused on the specific ditto traders and not so much on someone casual who put together a box of dittos because he was bored and wanted to sell them.
and if you are a specific ditto trader you will have everything arranged to choose X box of dittos, I don't think that whoever is dedicated to this will have them scattered in different boxes mixed with other pokemon.
and at most, the system should have a specific button that lets you see your list of boxes or better yet, when you press that button, it should open the "my pc" tab and you can manage it normally, with the option of "multiselect" and all that, so many errors would be avoided.