Drinfeld's gerbe isomorphism conjecture for truncated Barsotti–Tate groups

Let $G=GL(d)$ with the ${\mathbb G}_m$-action specified in the source. Let $\operatorname{BT}_{1,\mathbb F_p}^G$ be the paper's stack and let $\operatorname{BT}_1^{d,d'}\otimes\mathbb F_p$ be the stack of $1$-truncated Barsotti–Tate groups of height $d$ and dimension $d'$. Assuming the preceding identification of the two banding group schemes, these are gerbes over $\operatorname{Disp}_1^G$ banded by the same group scheme $\operatorname{Lau}_1^G$.

Drinfeld's gerbe isomorphism conjecture. These two gerbes are isomorphic.

This is the gerbe-level comparison underlying the proposed identification with the classical Barsotti–Tate stack. The source gives no resolution.