Savage–Visontai equidistribution conjecture for signed multiset permutations

Let $s=(1,4,3,8,5,12,\ldots)$, with $s_{2i}=4i$ and $s_{2i-1}=2i-1$ for $i\geq 1$. Let $I_n$ be the set of $s$-inversion sequences of length $n$, and let $P_n$ be the set of signed permutations on the multiset $\{1^2,2^2,\ldots,n^2\}$. Savage–Visontai conjecture. For every $n\geq 1$, the descent number over $P_n$ is equidistributed with the ascent number over $I_{2n}$. This conjecture would imply the real-rootedness of the generating function for the descent number over $P_n$; the cited context states that real-rootedness is known for ascent-number generating functions over arbitrary $s$-inversion sequences.