Exact lowest degree conjecture for Schur Q-functions

Let $\lambda$ be a strict partition, and let $Q_{\lambda}$ be the Schur Q-function. Give each power sum symmetric function degree $1$, so that $\deg(p_{\nu})=\ell(\nu)$. Let $\operatorname{srank}(\lambda)$ denote the shifted rank of $\lambda$. Exact lowest degree conjecture. The terms of lowest degree in $Q_{\lambda}$ have degree exactly $\operatorname{srank}(\lambda)$. This strengthens the preceding lower bound on the lowest degree of $Q_{\lambda}$; it has been computationally verified for all partitions $\lambda\vdash n$ with $1\leq n\leq 12$, but no general proof is given here.