It's a cone derived from a pine, thus pine-cone. However, I see your logic and support it. And as I said (and have just proven) I'm all for breaking the language. It's just that for me visually, it looks less like a compound noun and more like a torpedo. 
It's not a cone!
No, it's not really a cone at all is it; more like an ovoid.
Pine-Ovoid then?
Pine-Ovoid then?
Glad that's settled then.
Thank you for your superior shape knowledge.I think you were the one who identified the lack of conishness. 