Three-dimensional, commensurate long-range magnetic order in La2CuO4 quickly evolves to quasi-two-dimensional, incommensurate correlations upon doping with mobile holes, and superconductivity follows for x as small as 0.05 in the La2−xSrx/BaxCuO4 family of superconductors. The onset of superconductivity in these systems is known to be coincident with a remarkable rotation of the incommensurate spin order from “diagonal stripes” below x = 0.05 to “parallel stripes” above. However, little is known about the spin correlations at optimal and high doping levels, around and beyond the proposed quantum critical point for the pseudogap phase, p∗. Here, we present elastic and inelastic neutron scattering measurements on single crystals of La1.6−xNd0.4SrxCuO4 with x = 0.125, 0.19, 0.24, and 0.26 and show that two-dimensional, quasistatic, parallel spin stripes have an onset at temperatures such that the parallel spin stripe phase extends beyond p∗ and envelops the entirety of superconducting ground states in this system. We also show that the elastic order parameter for parallel spin stripes at optimum doping, x = 0.19, displays an inflection point at superconducting Tc, while the low-energy dynamic spectral weight of parallel stripe fluctuations grows with decreasing temperature and saturates below Tc.