Conjecture on derangement proportions in affine symplectic and orthogonal groups

Let $q$ be a prime power of odd characteristic, and let $m$ be a non-negative integer. For a finite group $G$ acting on a set, write $4\delta(G)4$ for the proportion of derangements in $G$. Let $\operatorname{ASp}_{2m}(q)$, $\operatorname{AO}_{2m+1}(q)$ and $\operatorname{AO}^{\pm}_{2m}(q)$ denote the affine symplectic and orthogonal groups in the indicated dimensions.

Derangement proportion conjecture. The following formulas hold:

$$\delta(\operatorname{ASp}_{2m}(q))=\frac{1}{q+1}\left(1-\frac{1}{(-q)^{m(m+2)}}\right).$$ $$\delta(\operatorname{AO}_{2m+1}(q))=\frac{1}{2}+\frac{(-1)^{m-1}}{2q^{(m+1)^2}}.$$ $$\delta(\operatorname{AO}^{\pm}_{2m}(q))=\frac{1}{2}\pm\frac{(-1)^{m-1}}{2q^{m(m+1)}}.$$

These formulas would give concise closed expressions for the derangement proportions in the affine symplectic and orthogonal cases. The paper reduces their proof to three $q$-polynomial identities, which are stated separately as Conjecture identities; the supplied text does not establish those identities or resolve this conjecture.