The unrestricted validity conjecture for Theorem a-f

Let $n$ be a positive integer, let $a,b,k$ be arbitrary nonnegative integers, and let $m,n_0\leq n\leq m+n_0$. Theorem a-f asserts a specific constant-term product formula for $\operatorname{CT}[\mathcal L_q(x_0,\boldsymbol{x};\boldsymbol{B}_{\mathcal A\mathcal F})]$, as displayed in the source. The unrestricted validity conjecture for Theorem a-f. The same theorem remains valid without the restriction

$$n\leq m+n_0.$$

The restriction is crucial to the proof given in the paper, although the authors state that it does not seem necessary. Thus the conjecture proposes extending the theorem's already established product formula to the full range $m,n_0\leq n$ without that restriction; the source gives no resolution evidence.