DAHA super-polynomial evaluation conjecture

Let $b\in P_+$ correspond to a Young diagram $\mu_b$ with rows of lengths $m_i$, and let $b_i=m_i\omega_1$. Write $\operatorname{ord}$ for the order of $\mu_b$. Evaluation conjecture. The specialization at $t=1$ satisfies

$$H\!D_{r,s}(b;q,t=1,a)=\prod_i H\!D_{r,s}(b_i;q,t=1,a),$$

and

$$H\!D_{r,s}(b_i;q=1,t=1,a)=\left(H\!D_{r,s}(\omega_1;q=1,t=1,a)\right)^{\operatorname{ord}}.$$

Moreover, when $0<s<r$, $\deg_a(H\!D_{r,s})=\operatorname{ord}(s-1)$. This gives multiplicative evaluation formulas for arbitrary Young diagrams, but the source does not establish them generally.