Monotonicity of maximal-orbit volume for the nearly Kähler families

Let $\{\Psi_a\}_{a>0}$ and $\{\Psi_b\}_{b>0}$ be the two one-parameter families of cohomogeneity-one nearly Kähler solutions, and let each solution have a maximal-volume orbit. Denote its volume by $V(\Psi_a)$ or $V(\Psi_b)$.

Monotonicity conjecture. The functions $V(\Psi_a)$ and $V(\Psi_b)$ are strictly increasing in $a$ and $b$, respectively.

The conjecture is motivated by numerical approximations; strict increase is known for the $\Psi_a$ family for sufficiently large $a$, while the global statement, including the $\Psi_b$ family, remains open.