(Thanks to CodeChic for this tip; see also WalruZ's similar thread.)
If you pick up a moving box and have it in your inventory, then the inventory search functionality will search over items in your moving boxes. It is then easier to move all of a certain type of item out of the moving box and into an SDB, for example.
(Inventory search is accessible via the little magnifying glass icon in the bottom left of the viewport; or by pressing the "~/`" key; or by pressing shift+F)
Items in moving boxes will also be available for crafting as well, as long as the box is in your inventory.