In the late stages of stellar core-collapse, prior to core bounce, electron captures on medium-heavy nuclei drive deleptonization and simulations require the use of accurate reaction rates. Nuclei with neutron number near N = 50, just above atomic number Z = 28, play an important role, but rates used in astrophysical simulations rely primarily on a relatively simple single-state approximation. In order to improve the accuracy of astrophysical simulations, experimental data are needed to test the electron-capture rates and to guide the development of better theoretical models. This work presents the results of the 86 Kr(t, 3 He+γ) experiment at the NSCL, from which an upper limit for the Gamow-Teller strength up to an excitation energy in 86 Br of 5 MeV is extracted. The derived upper limit for the electron-capture rate on 86 Kr indicates that the rate estimated through the single-state approximation is too high and that rates based on Gamow-Teller strengths estimated in shell-model and QRPA calculations are more accurate. The QRPA calculations tested in this manner were used for estimating the electron capture rates for 78 isotopes near N = 50 and above Z = 28. The impact of using these new electron-capture rates in simulations of supernovae instead of the rates based on the single-state approximation is investigated, indicating a significant reduction in the deleptonization that affects multi-messenger signals, such as the emission of neutrinos and gravitational waves.