The rank-two Betti-number generating-function conjecture for two torus actions

Let $P_q(X)=\sum_{i\geq0}\dim H_i(X)q^{i/2}$ be the Poincare polynomial, and consider the rank-two moduli spaces ${\mathcal M}(2,n)$ with the two fixed components corresponding to $T^{(0,0)}_{1,1}$ and $T^{(0,1)}_{1,1}$. Rank-two Betti-number conjecture.

$$\sum_{n\geq0}P_q\left({\mathcal M}(2,n)^{T^{(0,0)}_{1,1}}\right)t^n=\prod_{4\nmid i}\frac{1}{(1-t^i)(1-qt^i)}\prod_{i\geq1}\frac{1}{(1-qt^{4i})(1-q^2t^{4i})},$$

and

$$\sum_{n\geq0}P_q\left({\mathcal M}(2,n)^{T^{(0,1)}_{1,1}}\right)t^n=\prod_{n\geq1}\frac{1-t^{4n-2}}{(1-t^{2n-1})^2(1-qt^{4n-2})^2(1-q^2t^{4n-2})(1-qt^{4n})^2}.$$

This is proposed as the rank-two analogue of the earlier Betti-number formula; the supplied text does not state whether it has been proved or disproved.