>>12656509I think you're not considering a bunch of important factors.
Take your image of mass spectrometry. It uses an electromagnetic field and determines charge/mass ratios by fixing that component of the interaction (reasonably well) and letting small differences of mass affect the trajectory. It's not gravity that's causing the bulk of the deflection.
In your experimental setup, you would have to have an EM accelerator and then a vacuum chamber COMPLETELY SHIELDED from EM, due to the difference in magnitude of the forces you're testing for.
The point is, in the same setup, electron WOULDN'T fall down. Surely they do theoretically, but their charge has a way bigger effect and makes them fall anywhere (in terms of the detector.)