I am swimming in deep water here, but isn't it possible to define some notion of "gravity conservation" by considering the topological invariants of the spacetime in question ? In particular I am thinking of the ( generalised ) Gauss-Bonnet theorem here, which connects a measure of total curvature with the Euler characteristic of the manifold; the latter being a topological invariant means that there is a constraint as to how curvature can evolve over time. If you start with a particular gravitational set-up, then it is certainly possible to distort the spacetime manifold in various ways, but you can do so only in a manner that preserves the Euler characteristic.
In that sense, could one not define some concept of "total curvature" ( in the context of GR ) that is in fact a conserved quantity ? This is easily visualised by taking a sphere - you can twist, distort and deform that sphere in any which way you want, but no matter what you do, you will never be able to deform it into a flat plane, i.e. you will never be able to completely eliminate the curvature that was intrinsic to the manifold when you started. The same should be true for gravity - you cannot locally "eliminate" it, the most you can do is spread it out as gravitational radiation.
However, it seems that the theorem can be extended to cover pseudo-Riemannian manifolds as well, so long as they are orientable :