The left-eigenvector weighted-sum conjecture for the level-one D_r qKZ solution

At the Razumov–Stroganov point $q=e^{2i\pi/3}$ and in the homogeneous limit $w_i=1$, let $\Psi$ be normalized so that its smallest entry is $\Psi_{\pi_0}=1$. Let $v$ be the left eigenvector of $H_C$ with the same eigenvalue, namely $r$ for odd $r$ and $r+1/2$ for even $r$, normalized so that its entries are coprime positive integers. Left-eigenvector weighted-sum conjecture. The weighted sum of the entries of $\Psi$ is

$$\sum_\pi v_\pi\Psi_\pi=A(r).$$

This is an empirical identity relating the level-one $D_r$ $q$KZ ground-state vector to the number $A(r)$ of alternating sign matrices of size $r$; the source reports the formula but gives no proof or resolution.