The joint Destop-Desbot Wilf-equivalence conjecture for 3142, 3241, and 4132

For a permutation $\tau$, let $\operatorname{Destop}(\tau)$ and $\operatorname{Desbot}(\tau)$ denote its descent top and descent bottom sets. Patterns are $(\operatorname{Destop},\operatorname{Desbot})$-Wilf equivalent when their avoidance classes have the same joint distribution of these two statistics for every permutation length. The joint Destop-Desbot conjecture. The patterns $3142$, $3241$, and $4132$ are $(\operatorname{Destop},\operatorname{Desbot})$-Wilf equivalent. The source says this conjecture, together with the preceding classification conjectures, would identify the unique non-singleton joint equivalence class in $S_4$; the joint conjecture was verified computationally for avoiders of length at most $10$.