Defant–Kravitz's bound for tangled labelings of posets

Let $P$ be an $n$-element poset. A labeling of $P$ is tangled if its sorting time is $n-1$.

Defant–Kravitz's conjecture. $P$ has at most $(n-1)!$ tangled labelings.

This conjecture, attributed to Defant and Kravitz, concerns a sharp universal bound on tangled labelings; the paper reports partial progress toward it, but it remains open.