  We present numerical results for the gravitational self-force and redshift
invariant calculated in the Regge-Wheeler and Easy gauges for circular orbits
in a Schwarzschild background, utilizing the regularization framework
introduced by Pound, Merlin, and Barack. The numerical calculation is performed
in the frequency domain and requires the integration of a single second-order
ODE, greatly improving computation times over more traditional Lorenz gauge
numerical methods. A sufficiently high-order, analytic expansion of the
Detweiler-Whiting singular field is gauge-transformed to both the Regge-Wheeler
and Easy gauges and used to construct tensor-harmonic mode-sum regularization
parameters. We compare our results to the gravitational self-force calculated
in the Lorenz gauge by explicitly gauge-transforming the Lorenz gauge
self-force to the Regge-Wheeler and Easy gauges, and find that our results
agree to a relative accuracy of $10^{-15}$ for an orbital radius of $r_0=6M$
and $10^{-16}$ for an orbital radius of $r_0=10M$.
