We demonstrate the applicability of covariance analysis to three-dimensional velocity-map imaging experiments using a fast time stamping detector. Studying the photofragmentation of strong-field doubly ionized D2O molecules, we show that combining high count rate measurements with covariance analysis yields the same level of information typically limited to the "gold standard" of true, low count rate coincidence experiments, when averaging over a large ensemble of photofragmentation events. This increases the effective data acquisition rate by approximately 2 orders of magnitude, enabling a new class of experimental studies. This is illustrated through an investigation into the dependence of three-body D2O2+ dissociation on the intensity of the ionizing laser, revealing mechanistic insights into the nuclear dynamics driven during the laser pulse. The experimental methodology laid out, with its drastic reduction in acquisition time, is expected to be of great benefit to future photofragment imaging studies.