Even-odd monotonicity conjecture for orientation-reversing stretch factors

Let $S_g$ be the closed orientable surface of genus $g$, and let $\delta^+_{\mathrm{rev}}(S_g)$ be the minimal stretch factor among orientation-reversing pseudo-Anosov homeomorphisms of $S_g$ with orientable invariant foliations.

Even-odd monotonicity conjecture. For all $k\geq 1$,

$$\delta^+_{\mathrm{rev}}(S_{2k})>\delta^+_{\mathrm{rev}}(S_{2k-1}).$$

The conjecture asserts strict increase at every even-to-odd genus comparison and is motivated by the failure of strict decrease at every other step in the computed data. It remains open.