Distinct tame root types determine distinct braid-group orbits

Let $Q$ be the quiver under consideration, let $n$ be its number of vertices, let $\mathcal{E}$ be the set of exceptional sequences in question, and let $B_{n-1}$ act on $\mathcal{E}$. An element of $\mathcal{E}$ has tame type when its associated root type is tame.

Root-type orbit conjecture. Let $E_1,E_2\in\mathcal{E}$. Assume that there are $g_1,g_2\in B_{n-1}$ such that $g_1E_1$ and $g_2E_2$ have tame type but different root types. Then $E_1$ and $E_2$ lie in distinct orbits under $B_{n-1}$.

If true, this would show that different tame root types distinguish braid-group orbits of exceptional sequences. The source presents the assertion as an unknown generalization of the observation that, when $n=3$, minimal root types correspond exactly to tame full subquivers of $Q$; its status is therefore open.