  We prove the nonvanishing of the twisted central critical values of a class
of automorphic $L$-functions for twists by all but finitely many unitary
characters in particular infinite families. While this paper focuses on
$L$-functions associated to certain automorphic representations of unitary
groups, it illustrates how decades-old nonarchimedean methods from Iwasawa
theory can be combined with the output of new machinery to achieve broader
nonvanishing results. In an appendix, which concerns an intermediate step, we
also outline how to extend relevant prior computations for $p$-adic Eisenstein
series and $L$-functions on unitary groups to the case where primes dividing
$p$ merely needs to be unramified (whereas prior constructions required $p$ to
split completely) in the associated reflex field.
