Unimodality conjecture for the even part of reciprocal subsum numerators

Let $\mathrm{num}(n,x)$ be the numerator polynomial associated with sums of reciprocals of subsum polynomials over partitions of $n$, and write

$$\mathrm{num}(n,x)=\mathrm{num}_0(n,x)+\mathrm{num}_1(n,x),$$

where $\mathrm{num}_0(n,x)$ is even and $\mathrm{num}_1(n,x)$ is odd. Unimodality conjecture. The polynomial $\mathrm{num}_0(n,x)$ is unimodal. The paper reports experimental evidence for this conjecture, which remains open.