Dankelmann–Swart–Oellermann conjecture on Steiner diameter of highly connected graphs

Let $C_n^{2k}$ denote the $2k$-th power of the cycle $C_n$. Let $G$ be a $2k$-connected graph of order $n$. Dankelmann–Swart–Oellermann conjecture.

$$\operatorname{sdiam}_k(G)\leq \operatorname{sdiam}_k(C_n^{2k}).$$

This conjectures that the $2k$-th power of the cycle maximizes the Steiner $k$-diameter among $2k$-connected graphs of order $n$, generalizing the stated extremal result for $2$-connected graphs. The supplied text gives no resolution.