Grimm–Ballew procedure conjecture on Young graph isomorphism

Let $d_1,d_2\in\mathbb{Z}^+$ and let $m$ satisfy the Grimm–Ballew procedure's conditions; let $g_1$ and $g_2$ be different bases obtained by that procedure for the same $d_1$, $d_2$, and $m$. Grimm–Ballew isomorphism conjecture. Then

$$Y(g_1,m)\cong Y(g_2,m).$$

The conjecture is motivated by examination of reverse multiples generated by the Grimm–Ballew procedure; no proof or resolution is stated.