Phase shifts for s-wave MM scattering in both the I = 0 and I = 2 channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of 32(3) x 64. These results support our recent 2021 study of direct CP violation in K -> pi pi decay, improving our earlier 2015 calculation. The phase shifts are determined for both stationary and moving MM systems, at three (I = 0) and four (I = 2) different total momenta. We implement several pi pi interpolating operators including a scalar bilinear "sigma" operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.