Conjectured filling-shape-Wilf-equivalences for consecutive patterns

For consecutive permutation patterns, write $\sigma\stackrel{fs}{\sim}\tau$ when $\sigma$ and $\tau$ are filling-shape-Wilf-equivalent, meaning that they are avoided by fillings of every Young board with the same prescribed empty rows and columns. Filling-shape-Wilf-equivalences conjecture. The following pairs of consecutive patterns are filling-shape-Wilf-equivalent:

$$1342\stackrel{fs}{\sim}1432,$$ $$2341\stackrel{fs}{\sim}2431,$$ $$3124\stackrel{fs}{\sim}3214,$$ $$4123\stackrel{fs}{\sim}4213.$$

These equivalences are suggested by computer searches over Young boards of width at most $8$ and are proposed as further examples beyond the paper's proved results; they remain open.