OTOH, 2/3 of the neutrinos the standard fusion model predicts are MISSING...
Not anymore. They were found by the Sudbury Neutrino Observatory a few years ago.
It has been known for forty years that there are different "flavors" of neutrino. It has been known since the late '80's that there are three such flavors. SNO discovered that the reason early solar neutrino experiments only saw 1/3 of the neutrinos produced in the sun is that 2/3 of the solar neutrinos--which were all electron-type neutrinos when produced--were converted into muon- and tau-type neutrinos along the way. Early neutrino experiments were only sensitive to electron-type neutrinos, but SNO is sensitive to all three. SNO sees all of the neutrinos predicted by the standard solar model.