  Model-independent tests of gravity with cosmology are important when testing
extensions to the standard cosmological model. To maximise the impact of these
tests one requires predictions for the matter power spectrum on non-linear
scales. In this work we validate the \texttt{ReACT} approach to the non-linear
matter power spectrum against a suite of phenomenological modified gravity
N-body simulations with a time-varying gravitational constant, covering a wider
range of parameter space than previously examined. This vanilla application of
\texttt{ReACT} has limited range and precision due to the different
concentration-mass relation $c(M)$ that occurs when gravity is modified. We
extend this approach with a fitting function for a modified concentration-mass
relation, allowing for accurate (1$\%$) computation of the matter power
spectrum up $k=2\,h\,{\rm Mpc}^{-1}$ across a substantial range of parameter
space. This fitting function allows precision model-independent tests of
modified gravity to be carried out using the data from upcoming large scale
structure surveys.
