Conjecture on monotone triangle evaluations and vertically symmetric alternating sign matrices

Let $\alpha(n;k_1,\ldots,k_n)$ denote the number of monotone triangles with bottom row $(k_1,\ldots,k_n)$, extended to arbitrary integer bottom rows by the associated evaluation. For $n=2m+1$ with $m\geq 1$, consider the evaluations with bottom rows $(n,n-1,\ldots,1)$ and $(2,4,\ldots,2m)$. The monotone triangle evaluation conjecture.

$$\alpha(n;n,n-1,\ldots,1)=(-1)^m\alpha(m;2,4,\ldots,2m).$$

The absolute values of the left-hand evaluations are the numbers of vertically symmetric alternating sign matrices of odd order, while the right-hand side counts monotone triangles with prescribed bottom row $(2,4,\ldots,2m)$. The displayed identity is supported by the initial computed values, but its status is not resolved in the supplied text.