Grassmannian and bigrassmannian signed permutation avoidance conjecture

Let $S_n^B$ denote the group of signed permutations of size $n$. A signed permutation is Grassmannian if it has a unique descent, and bigrassmannian if both it and its inverse have a unique descent. For a signed pattern $p$, say that a signed permutation globally avoids $p$ when no subsequence, with arbitrary signs, has underlying pattern $p$. Define

$$P:=\{4321,32154,42153,43152,52143,53142,214365,315264,314265,415263\}.$$

Grassmannian and bigrassmannian avoidance conjecture. A signed permutation is Grassmannian if and only if it globally avoids every pattern in $P$, and it is bigrassmannian if and only if it globally avoids every pattern in

$$P\cup\{p^{-1}:p\in P\}.$$

This conjecture proposes finite global-pattern characterizations for two classes whose classical type-A characterizations do not directly persist for signed permutations. The statement is presented as a conjectural analogue of the known type-A pattern-avoidance results.