Defant and Zheng's maximal-time conjecture for the consecutive-pattern-avoiding stack-sorting map

Let $S_n$ be the set of permutations of length $n$, let $SC_{231}:S_n\to S_n$ be the stack-sorting map whose stack avoids consecutive occurrences of $231$, and let $\operatorname{Av}_n(132,231)$ denote the set of permutations in $S_n$ avoiding $132$ and $231$ consecutively. Defant and Zheng's conjecture. For any permutation $\pi$ of length $n\geq 3$,

$$SC_{231}^{2n-4}(\pi)\in \operatorname{Av}_n(132,231).$$

Also, for every $n\geq 3$, there exists $\tau\in S_n$ for which

$$SC_{231}^{2n-5}(\tau)\notin \operatorname{Av}_n(132,231).$$

The paper states this as a conjecture of Defant and Zheng and presents a counterexample, so the asserted universal claim is refuted; the first displayed bound is instead proved in the paper's main theorem.