Kadell's $q$-analogue of his constant-term hypothesis

Let $n$ be a positive integer, let $M\subset\{1,2,\dots,n\}$, and for each $s\in M$ choose an index $r_s$ such that $r_s\notin M$. Let $\boldsymbol{a}=(a_1,\dots,a_n)$ be nonnegative integers, and define $|\boldsymbol{a}|=\sum_{i=1}^n a_i$. For $1\leq i<j\leq n$, set

$$a_i^*=a_i^*(j)=a_i+\chi(j\in M, i=r_j),\qquad a_j^*=a_j^*(i)=a_j+\chi(i\in M, j=r_i).$$

With $(t)_k=(1-t)(1-tq)\dots(1-tq^{k-1})$, Kadell's $q$-analogue of his constant-term hypothesis. One has

$$\operatorname{CT}\left[\prod_{1\leq i<j\leq n}\left(\frac{x_i}{x_j}\right)_{a_i^*}\left(\frac{qx_j}{x_i}\right)_{a_j^*}\right]=\frac{1-q^{1+|\boldsymbol{a}|}}{1-q^{1+\sum_{v\notin M}a_v}}\genfrac{[}{]}{0pt}{}{|\boldsymbol{a}|}{\boldsymbol{a}}.$$

Kadell's earlier, more general non-$q$ hypothesis had recently been established by Zhou, but the source gives no resolution evidence for this $q$-analogue. Its significance is that it refines Dyson-type constant-term identities by prescribing contributions associated with the subset $M$.