Two-parameter Borwein positivity conjecture for $A_{L,m}(q)$ and $C_{L,m}(q)$

For nonnegative integers $L$ and $m$, let $A_{L,m}(q)$ and $C_{L,m}(q)$ be the polynomials defined by the finite multisums immediately preceding the claim. The index ranges are $0\leq m\leq L$ for $A_{L,m}(q)$ and $0\leq m\leq L-1$ for $C_{L,m}(q)$.

Two-parameter Borwein positivity conjecture. The polynomials $A_{L,m}(q)$ for $0\leq m\leq L$ and $C_{L,m}(q)$ for $0\leq m\leq L-1$ have nonnegative coefficients.

These polynomials refine the original Borwein polynomials through $A_L(q)=\sum_{m=0}^L A_{L,m}(q)$ and $C_L(q)=\sum_{m=0}^{L-1}C_{L,m}(q)$. The source gives no resolution status.