Since you cannot fire the kiln on its side, find a way to support the sculpture while it is upright. You could make a stand out of the same clay body. A flat slab the same length and width as the sculpture, with support wedges on the back, so the sculpture sits at a slight angle. That way it would fit, but not have the full weight of the sculpture pushing on itself.
You could also use crumpled newspaper stuff in the back. This would help transport the ware into the kiln, but obviously the supports would be gone, once the paper burned out.
You can lean things against the kiln walls, but it's not ideal. Personally, I'd go with my first suggestion. A custom support would work best. I've done it for myself and my students on a number of occasions.