Veselovac's stackability conjecture for complete binary trees

Let $T_h$ be the complete binary tree with depth $h$.

Veselovac's conjecture. The tree $T_h$ is stackable for all $h\ge 1$.

This conjecture was verified by Veselovac for $h\le 3$, and for the root vertex only when $h\le 5$; the general case remains open.