This idea is driven by my experience with an item sorter. I dumped my inventory into a storage container, it was draining to a sorting line and things that couldn't be sorted were sent back.
It ended up with leaves being sent to the belt, being rejected by the sorting line and the feedback belt was topping up that same item stack indefinitely, the outgoing items never reached any of the other items I dumped to the container.
Storage container feeding a belt should not use the same strategy used for player's inventory (e.g. when building). Instead, it should scan through all its inventory slots. When it starts feeding the belt from certain slot, it will make note how many items are in the stack at that moment and will only feed that many items from that slot regardless whether the stack gets topped up or not. Then it proceeds to the next slot.
I believe this strategy would not affect any of the current ways storage containers are used but will allow new use cases for storage containers containing multiple different items.