First of all I'd just like to say: I love this exercise. It took a bit to get used to the inversion, but they're seriously my favourite thing to train right now.
Something I've been wondering though: am I supposed to be pushing directly up and down? If I try to focus on this, (which requires some movement deeper into the pike) I find this causes me to perform a calf raise at the same time as the pushup. If focus on pushing entirely from my arms, I move towards my feet and the pike stays the same.
So the first way is clearly more complicated than the second, but I find it slightly easier. Surely the point of pushing vertically is to up the intensity, so does it matter which way I do this?