I'd love to see a cost summary of a typical lithium ion battery if you have it. How much is labor, energy, materials?

Depends entirely on the chemistry, but it's mainly Cobalt that is killing the price. Everyone tries to cut it out as much as possible. Tesla is trying to cut costs with less Cobalt but in general it means worse performance and a lot of safety issues with overheating or exploding. Huge amount of savings from the last years comes from cutting Cobalt by making better chemistries, trying to keep the safety record at the same time.