Wheel and broken-wheel cohomology conjecture over $\mathcal A_5$

For $n>4$, let $W_n$ be the wheel graph, let $W_n^{out}$ be obtained by deleting an edge from its polygonal part, and let $W_n^{in}$ be obtained by deleting a spike edge. Wheel and broken-wheel conjecture.

$$H^{1,4n-3}_{{\mathcal A}_5}(W_n^{out})=\mathbb{Z}_5^{n-1}\oplus\mathbb{Z}^{n-2}$$ $$H^{1,4n-3}_{{\mathcal A}_5}(W_n)=\mathbb{Z}_5^{n}\oplus\mathbb{Z}^{n}$$ $$H^{1,4n-3}_{{\mathcal A}_5}(W_n^{in})=\mathbb{Z}_5^{n-2}\oplus\mathbb{Z}^{n-2}.$$

These formulas are computational conjectures for $n>4$; the source does not report a resolution.