Unbalanced Wilf-equivalence conjecture for inversion-sequence pattern pairs

For a tuple of patterns, write $(\rho_1,\ldots,\rho_k)\thicksim(\sigma_1,\ldots,\sigma_\ell)$ when the corresponding inversion-sequence avoidance classes are Wilf-equivalent, meaning they have equal cardinality in every length. Unbalanced Wilf-equivalence conjecture. The following Wilf-equivalences hold:

$$(011,201)\thicksim(011,210)\thicksim(110,210,120,010)\thicksim(100,210,120,010).$$

The first equivalence has been confirmed in the paper, and the third was established by Martinez and Savage; the supplied status evidence therefore leaves the remaining conjectural equivalence unresolved.