Let's just assume, for now, that I don't have to explain WHY I want this. But...
I want a storage silo that works opposite of gravity. Items enter at the bottom and percolate up to the top chest and fill it. When the top chest is full, the one below starts to fill up. If somebody removes items from the top chest, items from below bubble up to keep the top chest filled.
Can it be done? Can it be done in a respectable footprint?
Assuming you don't want to get into command blocks:
One would need to monitor the fullness of the ouput chest (top chest) via a comparator output. [This would require at least one of the orthogonal neighbors of the chest (4 for 1/2 chest 6 for a full chest) to be either the comparator or a solid block; the only alternative I can see would be to continuously attempt to push items from a dropper below the chest which would "squirt out" the sides when the chest was full.]
That comparator output would activate a dropper pipe to push items into the chest until the chest was full – either up or from a side space not occupied by the comparator. [In order to avoid losing items from overfilling, the speed of the clock powering the dropper would need to be low.]
The input for the dropper pipe would most conveniently be a hopper line fed by a conventional top down silo.
[Stacking several chests each fed from below would not be possible at all as removing items from a chest would require a hopper beneath the chest.]
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WARNING: I have an extemely "grindy" playstyle; YMMV — if this doesn't seem fun to you, mine what you can from it & bin the rest.