Infinite ultrametric extension conjecture with four-point obstructions

Let $(X,d)$ be an infinite ultrametric space. A metric space is weakly similar to another when there is a similarity between them, allowing a positive rescaling of distances. Infinite extension conjecture. The following statements are equivalent:

1. There exists $(X^*,d^*)\in{\bf US}$ such that $(X,d)$ is isometric to a subspace of $(X^*,d^*)$.
2. $(X,d)$ contains no four-point subspace which is weakly similar to $(X_4,d_4)$ or to $(Y_4,\rho_4)$.

The source notes that the conjecture is true when $(X,d)$ is compact and that implication (1) $\Rightarrow$ (2) holds for arbitrary infinite ultrametric spaces; the unresolved part is implication (2) $\Rightarrow$ (1) for noncompact spaces.