The supernova (SN) neutronization phase produces mainly electron (nu(e)) neutrinos, the oscillations of which must take place within a few mean free paths of their resonance surface located nearby their neutrinosphere. The latest research on the SN dynamics suggests that a significant part of these nu(e) can convert into right-handed neutrinos by virtue of the interaction of the electrons and the protons flowing with the SN outgoing plasma, whenever the Dirac neutrino magnetic moment is of strength mu(nu) 10(-11) mu(B), with mu(B) being the Bohr magneton. In the SN envelope, some of these neutrinos can flip back to the left-handed flavors due to the interaction of the neutrino magnetic moment with the magnetic field in the SN expanding plasma (see the work by Kuznetsov & Mikheev; Kuznetsov, Mikheev, & Okrugin; Akhmedov & Khlopov; Itoh & Tsuneto; and Itoh et al.), a region where the field strength is currently accepted to be B greater than or similar to 10(13) G. This type of nu oscillation was shown to generate powerful gravitational wave (GW) bursts (see the work by Mosquera Cuesta; Mosquera Cuesta & Fiuza; and Loveridge). If such a double spin-flip mechanism does run into action inside the SN core, then the release of both the oscillation-produced nu(mu) and nu(tau) particles and the GW pulse generated by the coherent nu spin-flips provides a unique emission offset Delta T(GW <->nu)(emi) = 0 for measuring the nu travel time to Earth. As massive nu particles get noticeably delayed on their journey to Earth with respect to the Einstein GW they generated during the reconversion transient, then the accurate measurement of this time-of-flight delay by SNEWS + LIGO, VIRGO, BBO, DECIGO, etc., might readily assess the absolute nu mass spectrum.