Understanding and control of ultrafast non-equilibrium processes in semiconductors is key to making use of the full photon energy before relaxation, leading to new ways to break efficiency limits for solar energy conversion. In this work, we demonstrate the observation and modulation of slow relaxation in uniformly mixed tin-lead perovskites (MASnxPb1-xI3 and CsSnxPb1-xI3 nanocrystals). Transient absorption measurements reveal that slow cooling mediated by a hot phonon bottleneck effect appears at carrier densities above ~1018 cm-3 for tin-lead alloy nanocrystals, and tin addition is found to give rise to suppressed cooling. Within the alloy nanoparticles, the combination of a newly introduced high-energy band, screened Fröhlich interaction, suppressed Klemens decay and reduced thermal conductivity (acoustic phonon transport) with increased tin content contributes to the slowed relaxation. For inorganic nanocrystals where defect states couple strongly with carriers, sodium doping has been confirmed to benefit in maintaining hot carriers by decoupling them from deep defects, leading to a decreased energy-loss rate during thermalization and an enhanced hot phonon bottleneck effect. The slow cooling we observe uncovers the intrinsic photophysics of perovskite nanocrystals, with implications for photovoltaic applications where suppressed cooling could lead to hot-carrier solar cells.