Monotonicity conjecture for the period length of SOPS to Wright's equation

Let $x$ be a slowly oscillating periodic solution (SOPS) of Wright's equation

$$x'(t)=-\alpha f(x(t-1)),$$

with parameter $\alpha$ and period length $L(\alpha)$. Monotonicity conjecture. The period length of SOPS to Wright's equation increases monotonically in $\alpha$. This question concerns how the periods of slowly oscillating periodic solutions vary with the parameter in Wright's equation. The source states that the conjecture remains unresolved for $\alpha>\tfrac{\pi}{2}+6.830\times10^{-3}$, so it is open.