Conjecture on non-isomorphism of universal ambits for closed subgroups of $S_\infty$

Let $G$ be a closed, non-compact subgroup of $S_\infty$ whose universal minimal flow $M(G)$ is metrizable. Consider the universal ambit $S(G)$ and the enveloping semigroup $E(M(G))$.

Non-isomorphism conjecture.

$$S(G)\not\cong E(M(G)).$$

This is presented as a strict sub-conjecture of Pestov's conjecture and is suggested as a potentially more approachable version. The source does not provide evidence that it has been resolved.