The split-permutation conjecture for largest MVP fibre size

For $n\geq 1$, let $\mathcal{O}_{\mathrm{MVP}_{n}}$ denote the MVP outcome map on permutations of size $n$, and let $\mathrm{split}^{2,n-2}:=(n-1)n(n-2)(n-3)\cdots21$ for $n\geq3$. The MVP split-permutation conjecture. For $n\geq6$, the permutation with the largest MVP fibre size is the split permutation $\mathrm{split}^{2,n-2}$. Numerical evidence supports the claim for $n=7,8,9,10,11$, although the conjecture is not established in the supplied text.