  This article continues our study of $P$- and $Q$-key polynomials, which are
(non-symmetric) "partial" Schur $P$- and $Q$-functions as well as "shifted"
versions of key polynomials. Our main results provide a crystal interpretation
of $P$- and $Q$-key polynomials, namely, as the characters of certain connected
subcrystals of normal crystals associated to the queer Lie superalgebra
$\mathfrak{q}_n$. In the $P$-key case, the ambient normal crystals are the
$\mathfrak{q}_n$-crystals studied by Grantcharov et al., while in the $Q$-key
case, these are replaced by the extended $\mathfrak{q}_n$-crystals recently
introduced by the first author and Tong. Using these constructions, we propose
a crystal-theoretic lift of several conjectures about the decomposition of
involution Schubert polynomials into $P$- and $Q$-key polynomials. We verify
these generalized conjectures in a few special cases. Along the way, we
establish some miscellaneous results about normal $\mathfrak{q}_n$-crystals and
Demazure $\mathfrak{gl}_n$-crystals.
