The negative Hall voltage is strictly a consequence of electrons being waves.
QM is the proper explanation to our world, no alternative is in sight, all others fail. So make peace with it and learn it, it's fascinating.
By Einstein, you mean reject the random nature of particles and hope for hidden variables? This has been proven false and even impossible, experimentally. Old Albert was wrong on this point. Forget it.
Electrons can have a negative or positive mass in solids, and this mass differs numerically from the one in vacuum. Not only Hall measures tell it. All semiconductor components that process light (LED, laser diodes, detectors, germanium lenses...) rely on this "effective mass", sometimes in a very subtle manner. Semicon engineers use it to make predictions that are verified at the components. Every single DVD burner is a proof of it.
You write "nuclei would repel an electron with negative mass" but an electron with an effective mass pertains to a band, hence is already delocalized over many nuclei. Which nucleus should repel the electron toward what nucleus-free direction? It seems that you'd like to imagine electrons as point-like particles, and this misconception leads you directly into wrong deductions.
You can look for positive "hall coefficients" in metals:
http://www.ifsc.usp.br/~lavfis/BancoApostilasImagens/ApEfHall-CondEletr/EfHallMetals-5_3_03.pdfhttp://www.phys.utk.edu/labs/modphys/Hall%20Effect.pdf page 8
for instance iron, zinc, cobalt, molybdenum... have a positive coefficient resulting from the negative mass.
Hall experiments are usually made with semiconductors to have fewer charge carriers, which are then faster for a given current and give a higher Hall voltage. If using a metal, whose carrier density is huge, a thin foil improves the situation; the Hall voltage stays small and difficult to observe. I suggest to cable everything, then place or remove a permanent magnet and try to observe a voltage variation - a few microvolts with thin foils.