If there were electrons with a positive charge, we'd expect them to have shown up in experiments like the Millikan oil drop experiment, and similar experiments that have been used to measure the charge of an electron. In that case, the gravitational force is exerted on the entire drop of oil (the electrons themselves provide an insignificant fraction of the mass involved), so it wouldn't make a difference whether the electron's mass were positive or negative. That type of experiment determines the absolute charge, not just a charge to mass ratio.
Conserve energy. Commute with the Hamiltonian.