Consistency of Hamiltonian reduction of Einstein's equations

I show that the recently proposed Hamiltonian reduction of general relativity of 4 dimensional spacetimes with no isometries is consistent with general covariance, although Hamilton's equations of motion that follow from the non-zero gravitational Hamiltonian are written in the privileged coordinates. The consistency is established by showing that Hamilton's equations that follow from the non-zero gravitational Hamiltonian are identical to Einstein's equations written in the privileged coordinates.