Solar neutrino flux constraints from the legacy GALLEX/GNO and SAGE experiments continue to influence contemporary global analyses of neutrino properties. The constraints depend on the neutrino absorption cross sections for various solar sources. Following recent work updating the Cr and Ar neutrino source cross sections, we reevaluate the Ga solar neutrino cross sections, focusing on contributions from transitions to Ge excited states, but also revising the ground-state transition to take into account new Ge electron-capture lifetime measurements and various theory corrections. The excited-state contributions have been traditionally taken from forward-angle cross sections. Here we correct this procedure for the tensor operator contribution that alters the relationship between Gamow-Teller and transition strengths. Using state-of-the-art nuclear shell-model calculations to evaluate this correction, we find that it lowers the B and hep neutrino cross sections. However, the addition of other corrections, including contributions from near-threshold continuum states that radiatively decay, leads to an overall increase in the B and hep cross sections of relative to the values recommended by Bahcall. Uncertainties are propagated using Monte Carlo simulations.