This.
Height makes things easier for us -- we don't have to bend down and hunch over -- and it makes it easier to ventilate -- we can get the vents well above the roosts more easily -- and it even helps with heat since it rises away from the birds (why old houses in hot climates have high ceilings).
But chickens don't stack for storage and they fly at about a 45-degree angle so they need room to get up and down.
The only report I've seen here of a vertical, multi-story type space working for chickens involves very active game bantams who fly more like wild birds than the wing-assisted leaps and falling with style that most dual-purpose breeds are limited to.
Do you have photographs of the area so we could visualize the space better?
My inclination would be to set it up as an open-air coop and plan to access it from the wide side as a reach-in rather than walk-in since it's so shallow.