Although SU(1,1) interferometry achieves Heisenberg-limited sensitivities, it suffers from one major drawback: Only those particles outcoupled from the pump mode contribute to the phase measurement. Since the number of particles outcoupled to these "side modes" is typically small, this limits the interferometer's absolute sensitivity. We propose an alternative "pumped-up" approach where all the input particles participate in the phase measurement and show how this can be implemented in spinor Bose-Einstein condensates and hybrid atom-light systems-both of which have experimentally realized SU(1,1) interferometry. We demonstrate that pumped-up schemes are capable of surpassing the shot-noise limit with respect to the total number of input particles and are never worse than conventional SU(1,1) interferometry. Finally, we show that pumped-up schemes continue to excel-both absolutely and in comparison to conventional SU(1,1) interferometry-in the presence of particle losses, poor particle-resolution detection, and noise on the relative phase difference between the two side modes. Pumped-up SU(1,1) interferometry therefore pushes the advantages of conventional SU(1,1) interferometry into the regime of high absolute sensitivity, which is a necessary condition for useful quantum-enhanced devices.