Morgan's conjecture on Steiner point degrees

Let $K$ be a centred convex body in $\mathbf{R}^d$. A $K$-Steiner minimal tree ($K$-SMT) is a Steiner tree of a finite point set having minimum total edge length in the norm $\lVert\cdot\rVert_K$. Let $s(K)$ be the maximum possible degree of a Steiner point in a $K$-SMT, and define

$$s(d):=\max\{s(K):K\in\mathcal{K}^d_o\}.$$

Morgan's conjecture. For all $d\geq 2$,

$$s(d)\leq 2^d.$$

The conjecture concerns the largest possible degree of a Steiner point in a Steiner minimal tree over all centred convex bodies in dimension $d$. The supplied text gives no resolution status.