  We develop methods for investigating baryon acoustic oscillation (BAO)
features in cosmological models with non-trivial (but slowly varying) averaged
spatial curvature: models that are not necessarily flat, close to flat, nor
with constant spatial curvature. The class of models to which our methods apply
include Lemaitre-Tolman-Bondi models, modified gravity cosmologies, and
inhomogeneous cosmologies with backreaction - in which we do not have a
prediction of the shape of the spatial 2-point correlation function, but where
we nevertheless expect to see a BAO feature in the present-day galaxy
distribution, in form of an excess in the galaxy 2-point correlation function.
  We apply our methods to the Baryon Oscillation Spectroscopic Survey (BOSS)
dataset, investigating both the Lambda Cold Dark Matter ($\Lambda$CDM) and
timescape cosmological models as case studies. The correlation functions
measured in the two fiducial models contain a similarly-pronounced BAO feature.
We use the relative tangential and radial BAO scales to measure the anisotropic
Alcock-Paczy\'nski distortion parameter, $\epsilon$, which is independent of
the underlying BAO preferred scale. We find that $\epsilon$ is consistent with
zero in both fiducial cosmologies, indicating that models with a different
spatial curvature behaviour can account for the relative positions of the
tangential and radial BAO scale. We validate our methods using $\Lambda$CDM
mocks.
