  The Problem of Time (PoT) is a multi-faceted conceptual incompatibility
between various areas of Theoretical Physics. Whilst usually stated as between
GR and QM, in fact 8/9ths of it is already present at the classical level. Thus
we adopt a `top-down' classical and then quantum approach. I consider a local
resolution to the Problem of Time that is Machian, which was previously
realized for relational triangle and minisuperspace models. This resolution has
three levels: classical, semiclassical and combined
semiclassical-histories-records. This article's specific model is a slightly
inhomogeneous cosmology considered for now at the classical level. This is
motivated by how the inhomogeneous fluctuations that underlie structure
formation - galaxies and CMB hotspots - might have been seeded by quantum
cosmological fluctuations, as magnified by some inflationary mechanism. In
particular, I consider the perturbations about $S^3$ case of this involving up
to second order, which has a number of parallels with the Halliwell-Hawking
model but has a number of conceptual differences and useful upgrades. The
article's main features are that the elimination part of the model's thin
sandwich is straightforward, but the modewise split of the constraints fail to
be first-class constraints. Thus the elimination part only arises as an
intermediate geometry between superspace and Riem. The reduced geometries have
surprising singularities influenced by the matter content of the universe,
though the N-body problem anticipates these with its collinear singularities. I
also give a `basis set' of Kuchar beables for this model arena.
