Have you tried reversing the stacking order? That is, Sorts on the top instead of the bottom? I know it would make it top heavy, and would require some attention when rolling, but it seems it might be better when you try to pick up the whole stack.
I also thought about suggesting a Ruxxac cart two-wheeler to negotiate the stairs, instead of carrying.
I also thought about suggesting a Ruxxac cart two-wheeler to negotiate the stairs, instead of carrying.