SE has shown us that they really only have one way to store items. The way we see in inventory, retainers and chocobo bags.
They may be able to do something like with the glamour dresser but with the limitations that has on taking things out I am not sure the system would work for tackle.
Perhaps it's better to do away with the items altogether and just give you the ability to select from all the possible baits and you would never run out?
Or just remove the vast majority of the baits/lures till you the amount is manageable.