  We introduce a subclass of recursive subhomogeneous algebras, in which each
of the pullback maps is diagonal in a suitable sense. We define the notion of a
diagonal map between two such algebras and show that every simple inductive
limit of these algebras with diagonal bonding maps has stable rank one. As an
application, we prove that for any infinite compact metric space $T$ and
minimal homeomorphism $h\colon T\to T$, the associated dynamical crossed
product $\mathrm{C^*}(\mathbb{Z},T,h)$ has stable rank one. This affirms a
conjecture of Archey, Niu, and Phillips. We also show that the Toms-Winter
Conjecture holds for such crossed products.
