Abstract: Measuring core-collapse supernova neutrinos, both from individual supernovae within the Milky Way and from past core collapses throughout the Universe (the diffuse supernova neutrino background, or DSNB), is one of the main goals of current and next generation neutrino experiments. Detecting the heavy -lepton flavor (muon and tau types, collectively nu x) component of the flux is particularly challenging due to small statistics and large backgrounds. While the next galactic neutrino burst will be observed in a plethora of neutrino channels, allowing us to measure a small number of nu x events, only upper limits are anticipated for the diffuse nu x flux even after decades of data taking with conventional detectors. However, paleo detectors could measure the time-integrated flux of neutrinos from galactic core-collapse supernovae via flavor-blind neutral current interactions. In this work, we show how combining a measurement of the average galactic core-collapse supernova flux with paleo detectors and measurements of the DSNB electron -type neutrino fluxes with the next-generation water Cherenkov detector Hyper-Kamiokande and the liquid noble gas detector DUNE will allow to determine the mean supernova nu x flux parameters with precision of order ten percent. Realizing this potential requires both the cosmic supernova rate out to z -1 and the integrated Galactic supernova rate over the last-1 Gyr to be established at the-10% level.