The refined qQTFPL enumeration product formula

For each size $n$, let $A(n;y)$, $A_{\textsc{HT}}(n;y)$, and $A_{\textsc{QT}}(n;y)$ denote the enumerating polynomials of FPLs, HTFPLs, and qQTFPLs, respectively. Give an object weight $y^k$, where $k$ is the index of the column, numbered from $0$ to $n-1$, containing the single nonzero entry in the first row of its alternating-sign matrix. The refined qQTFPL enumeration conjecture. For any $n\geq 1$,

$$A_{\textsc{QT}}(4n+2;y)=yA_{\textsc{HT}}(2n+1;y)A(n+1;y)A(n;y).$$

This is presented as a refinement of the preceding enumeration formula and as an extension of a further conjecture of Robbins. The source gives no resolution evidence beyond the surrounding exhaustive-enumeration motivation.