We consider crossed product C*-algebras of the form $C^{*}(\mathbb{Z},C(X,D),\alpha)$ for a compact metric space $X$ and an infinite-dimensional C*-algebra $D$. We show that, under appropriate conditions on $X$, $D$, and $\alpha$, such crossed products have tractable structure. In particular, if $D$ is purely infinite then so is $C^{*}(\mathbb{Z},C(X,D),\alpha)$, while if $D$ is $\mathcal{Z}$-stable, nuclear, and has a quasitrace, then $C^{*}(\mathbb{Z},C(X,D),\alpha)$ has nuclear dimension at most 1. We also give some results in cases where $D$ is not $\mathcal{Z}$-stable but $X$ is low-dimensional, and apply our results to examples which do not appear to be accessible through previously existing methods.

This is joint work with Dawn Archey and N. Christopher Phillips.