  In the era of precision cosmology, even percentage level effects are
significant on cosmological observables. The recent tension between the local
and global values of $H_0$ is much more significant than this, and any possible
solution might rely on us going beyond the standard $\Lambda$CDM cosmological
model. For much smaller, yet potentially significant effects, spatial curvature
from averaging and cosmological backreaction on observational predictions could
play a role. This is especially true with the higher precision of new
observational data and improved statistical techniques. In this paper, we
discuss the observational viability of a class of physically motivated
cosmologies which can be parametrized by a phenomenological two-scale
backreaction model with decoupled spatial curvature parameters and two Hubble
scales. Using the latest JLA Supernovae data together with some of the latest
BAO data, we perform a Bayesian model selection analysis and find that the
phenomenological models are not favoured over the standard $\Lambda$CDM
cosmological model. Although there is still a preference for non-zero and
unequal dynamic and geometric spatial curvatures, there is little evidence for
differing Hubble scales within these phenomenological template models.
