Shifted Plücker value log-concavity conjecture

Let $\lambda=(2^{e_2},\ldots,m^{e_m})$ be a partition without parts equal to $1$, set $N:=|\lambda|$ and $M:=|\widetilde\lambda|$, and write

$$[\overline Y_\lambda(d)]=\sum_{\lceil M/2\rceil\le i\le M}P_{\lambda;i}(d)s_{i,M-i}.$$

For each admissible pair $(\lambda,i)$, define $Q_{\lambda;i}(x):=P_{\lambda;i}(N+x)$. Shifted Plücker value log-concavity conjecture. For every admissible pair $(\lambda,i)$, the sequence

$$Q_{\lambda;i}(0),Q_{\lambda;i}(1),Q_{\lambda;i}(2),\ldots$$

is log-concave after deleting its initial zeroes. Equivalently,

$$P_{\lambda;i}(N+x)^2\ge P_{\lambda;i}(N+x-1)P_{\lambda;i}(N+x+1)$$

for all $x\ge1$ in the nonzero range. The source says this is a formally weaker consequence of the shifted-binomial conjecture and gives no resolution status.