Lin's symmetry conjecture for ascents of restricted inversion sequences

For $n\geq 1$, let $\mathbf{I}_n(\geq,\neq,>)$ and $\mathbf{I}_n(>,\neq,\geq)$ be the two classes of inversion sequences avoiding the indicated relation triples. For an inversion sequence $e$, let $\operatorname{asc}(e)$ be its number of ascents. Lin's symmetry conjecture.

$$\sum_{e\in\mathbf{I}_n(\geq,\neq,>)}t^{\operatorname{asc}(e)}=\sum_{e\in\mathbf{I}_n(>,\neq,\geq)}t^{n-1-\operatorname{asc}(e)}.$$

This predicts a palindromic correspondence between ascent distributions in the two inversion-sequence classes. The paper states that Lin's earlier bijection does not prove this symmetry, and no resolution is supplied in the provided text.