Beam-target double-spin asymmetries and target single-spin asymmetries were measured for the exclusive π 0 electroproduction reaction γ * p → pπ 0 , expanding an analysis of the γ * p → nπ + reaction from the same experiment. The results were obtained from scattering of 6 GeV longitudinally polarized electrons off longitudinally polarized protons using the CEBAF Large Acceptance Spectrometer at Jefferson Lab. The kinematic range covered is 1.1 < W < 3 GeV and 1 < Q 2 < 6 GeV 2 . Results were obtained for about 5700 bins in W , Q 2 , cos(θ * ), and φ * . The beam-target asymmetries were found to generally be greater than zero, with relatively modest φ * dependence.The target asymmetries exhibit very strong φ * dependence, with a change in sign occurring between results at low W and high W , in contrast to π + electroproduction. Reasonable agreement is found with phenomenological fits to previous data for W < 1.6 GeV, but significant differences are seen at higher W . When combined with cross section measurements, as well as π + observables, the present results will provide powerful constraints on nucleon resonance amplitudes at moderate and large values of Q 2 , for resonances with masses as high as 2.4 GeV.