Universal factorial Schur P and Q duality at beta equals minus one

Let $\lambda$ be a strict partition. Let $\widehat{p}^K_\lambda({\bf y})$ and $\widehat{q}^K_\lambda({\bf y})$ be the dual universal factorial Schur $P$- and $Q$-functions, and let $gp_\lambda({\bf y})$ and $gq_\lambda({\bf y})$ be the tableau-defined functions

$$gp_\lambda({\bf y})=\sum_{T\in Tab'(\lambda)}{\bf y}^T,\qquad gq_\lambda({\bf y})=\sum_{T\in Tab(\lambda)}{\bf y}^T.$$

The conjectural combinatorial formula. One has

$$gp_\lambda({\bf y})=\left.\widehat{p}^K_\lambda({\bf y})\right|_{\beta=-1},\qquad gq_\lambda({\bf y})=\left.\widehat{q}^K_\lambda({\bf y})\right|_{\beta=-1}.$$

The paper states that this is true for the one-row case, namely for every positive integer $k$.