The one-point extension conjecture for Euclidean Ramsey sets

Let $X\subset\mathbb R^d$ be a finite Ramsey set, and regard $\mathbb R^d$ as a hyperplane in $\mathbb R^{d+1}$. Let $z\in\mathbb R^{d+1}$ be a point outside that hyperplane.

One-point extension conjecture. The set $X\cup\{z\}$ is Ramsey.

The paper calls this an intriguing open problem. It would follow from either of the two competing conjectures that Ramsey sets are exactly the spherical sets or exactly the subtransitive sets.