Few-body nuclear physics often relies upon phenomenological models, with new efforts at the ab initio theory reported recently; both need high-quality benchmark data, particularly at low center-of-mass energies. We use high-energy-density plasmas to measure the proton spectra from ^{3}He+T and ^{3}He+^{3}He fusion. The data disagree with R-matrix predictions constrained by neutron spectra from T+T fusion. We present a new analysis of the ^{3}He+^{3}He proton spectrum; these benchmarked spectral shapes should be used for interpreting low-resolution data, such as solar fusion cross-section measurements.