Conjecture on Wilf-equivalence of vincular patterns 2314 and 1234

A vincular pattern is a permutation pattern in which selected adjacent entries are required to occur consecutively; write $\sigma\sim\tau$ when two patterns are Wilf-equivalent, meaning that they are avoided by the same number of permutations of every length. Wilf-equivalence conjecture. The vincular patterns $23\text{-}1\text{-}4$ and $1\text{-}23\text{-}4$ are Wilf-equivalent:

$$23\text{-}1\text{-}4 \sim 1\text{-}23\text{-}4.$$

Computations for permutations of length at most $11$ suggest that $23\text{-}1\text{-}4$ is an additional member of the equivalence class containing $1\text{-}23\text{-}4$; the equivalence remains open.