For me, N is small. Its also N-ary, not binary, which crosses off a bunch of the first options. Anyway, I am not sure this will work, just worth trying. Empirical numbers beat theory every time :)
You are using N in a different sense than I am. Unless I'm reading the tree description incorrectly, N is the size of the tree itself, not the number of children.
I would hazard a guess that a regular n-ary tree would outperform the OP tree in many usage scenarios with no extra effort, and with a number of B+ tree variants being strictly better at the cost of more effort.