Base-case conjecture for centrally extended orbits in finite models

Let $e$ be a nilpotent element in a classical Lie algebra $\mathfrak{g}$, with partition $\lambda$, and let $\lambda^\intercal$ be its dual partition. Form $\lambda_{\mathrm{red}}$ by removing $2l$ parts whenever a part of $\lambda^\intercal$ has multiplicity $2l+1$ or $2l+2$, and set $\lambda'=\lambda_{\mathrm{red}}^\intercal$. Let $e'$ be the corresponding nilpotent element in a Lie algebra of the same type, and let $Y_e,Y_{e'}$ be the associated finite models; under the natural identifications $Q_e\cong Q_{e'}$ and $A_e\cong A_{e'}$, compare their centrally extended orbits. Base-case conjecture. An $Q_e$-centrally extended orbit appears in $Y_e$ if and only if it appears in $Y_{e'}$. This predicts that the orbit structure for arbitrary partitions is determined by the reduced base cases; the supplied passage gives no resolution.