Sign conjecture for motivic Chern class coefficients in new positivity variables

Let $p,w$ be permutations, and expand the motivic Chern class $\mC[p]$ in the Schubert basis $\{\mathbf{[w]}\}$. Make the substitutions

$$\frac{\tau_i}{\tau_{i+1}}=s_i+1,\qquad y=-1-\delta.$$

The resulting coefficients are polynomials in the variables $s_i$ and $\delta$.

New-variable sign conjecture. The coefficients of the $s_i,\delta$-monomials in the $\mathbf{[w]}$-expansion of the $\mC[p]$ classes have sign $(-1)^{\ell(w)}$.

This sign pattern differs from the preceding conjecture because it depends only on the length of $w$, not on the length of $p$. The displayed examples support the conjecture, but the supplied text gives no general verification or resolution.