I've been getting quite a few helmet heads this year. (I was going to say something vaguely scandalous involving peter peppers, but I'll leave that to your imagination.)
I think I may have identified a source of the problem - seeds planted too shallow. Imagine how the seed sprouts. It sends down a root and pushes the end with the seed case still attached into the air, looking like a little fishhook with a guard (the seed case) over the pointy end. In effect, it pulls the case through the soil up into the air. If it were planted more deeply, the soil would offer more resistance to the case, possibly pulling the cots out before it breaks the surface. Further, the longer it is underground the more it remains moist and flexible.
When I've dissected my helmet heads, it looks like the seed was sitting little deeper than 1/8". I think I'll try planting deeper.