A system for operating a harvester may include an elevator extending between a proximal end and a distal end, with the elevator being configured to carry harvested crops between its proximal and distal ends. The system may also include a storage hopper positioned adjacent to the distal end of the elevator, with the storage hopper defining a volume configured to receive the harvested crops discharged from the distal end of the elevator. In addition, the system may include a rotary spreader positioned within the storage hopper. The rotary spreader may be configured to be rotated within the storage hopper to disperse the harvested crops received from the elevator across at least a portion of the volume.