  The $E_G$ statistic is a discriminating probe of gravity developed to test
the prediction of general relativity (GR) for the relation between
gravitational potential and clustering on the largest scales in the observable
universe. We present a novel high-precision estimator for the $E_G$ statistic
using CMB lensing and galaxy clustering correlations that carefully matches the
effective redshifts across the different measurement components to minimize
corrections. A suite of detailed tests is performed to characterize the
estimator's accuracy, its sensitivity to assumptions and analysis choices and
the non-Gaussianity of the estimator's uncertainty is characterized. After
finalization of the estimator, it is applied to $\textit{Planck}$ CMB lensing
and SDSS CMASS and LOWZ galaxy data. We report the first harmonic space
measurement of $E_G$ using the LOWZ sample and CMB lensing and also updated
constraints using the final CMASS sample and the latest $\textit{Planck}$ CMB
lensing map. We find $E_G^{Planck+CMASS} = 0.36^{+0.06}_{-0.05}$ (68.27%) and
$E_G^{\rm \textit{Planck}+LOWZ} = 0.40^{+0.11}_{-0.09} $ (68.27%), with
additional subdominant systematic error budget estimates of 2% and 3%
respectively. Using $\Omega_{\rm m,0}$ constraints from $\textit{Planck}$ and
SDSS BAO observations, $\Lambda$CDM-GR predicts $E_G^{\rm GR} (z = 0.555) =
0.401 \pm 0.005$ and $E_G^{\rm GR} (z = 0.316) = 0.452 \pm 0.005$ at the
effective redshifts of the CMASS and LOWZ based measurements. We report the
measurement to be in good statistical agreement with the $\Lambda$CDM-GR
prediction, and report that the measurement is also consistent with the more
general GR prediction of scale-independence for $E_G$. This work provides a
carefully constructed and calibrated statistic with which $E_G$ measurements
can be confidently and accurately obtained with upcoming survey data.
