The modular plethystic isomorphism for two-row partitions

Let $M,N\in\mathbb{N}$, let $d\in\mathbb{N}_0$, let $\mathbb{F}$ be the underlying field, and let $E$ be the natural $2$-dimensional $\mathbb{F}$-representation of $\operatorname{SL}_2(\mathbb{F})$. Write $\Delta^{(M,1^{N-1})}$ for the Weyl module associated with the partition $(M,1^{N-1})$. Modular plethystic isomorphism conjecture. There is an isomorphism of $\operatorname{SL}_2(\mathbb{F})$-representations

$$\bigwedge^{M-1} \operatorname{Sym}^{M+N-3}E\otimes\bigwedge^{M+N-1}\operatorname{Sym}^{M+d-1}E\cong\Delta^{(M,1^{N-1})}\operatorname{Sym}^dE.$$

The paper's main theorem proves the special case $M=2$; the asserted isomorphism for general $M$ is the conjectural extension.