The Gurarij space's WEMI and transitive-space conjecture

The Gurarij space is denoted by $\mathbf{G}$, and $\operatorname{Aut}(\mathbf{G})$ denotes its isometric automorphism group. A complete $\operatorname{Aut}(\mathbf{G})$-space is a complete metric space equipped with a continuous action of this group; it is transitive if the action has a single orbit. WEMI refers to the property that every weakly eliminating metric imaginary is equivalent to a metric imaginary.

Gurarij space conjecture. The Gurarij space $\mathbf{G}$ has WEMI, and every transitive complete $\operatorname{Aut}(\mathbf{G})$-space is a singleton.

The Gurarij space is a natural candidate because it is $\aleph_0$-categorical and eliminates quantifiers, while its automorphism group does not act transitively on each sphere. The source indicates that an explicit analysis of its imaginary sorts is expected to be possible, but does not establish the stated WEMI and transitive-space conclusions.