The $q$-rious unimodality conjecture

Let $(\boldsymbol{a},\boldsymbol{b})$ be tuples of positive integers satisfying Landau's criterion, namely

$$\sum_i\lfloor a_i x\rfloor-\sum_j\lfloor b_j x\rfloor\geqslant 0 \quad\text{for all }x\geqslant 0.$$

Let $D(\boldsymbol{a},\boldsymbol{b};q)$ be the corresponding $q$-factorial quotient, and write its coefficients as $D(\boldsymbol{a},\boldsymbol{b};q)=\sum_{i=0}^k c_iq^i$. $q$-rious unimodality conjecture. The polynomial

$$(1+q)D(\boldsymbol{a},\boldsymbol{b};q)$$

is unimodal. This is proposed as a stronger statement implying the $q$-rious positivity conjecture, in a setting where the coefficient sequence of $D(\boldsymbol{a},\boldsymbol{b};q)$ is symmetric.