Xris wrote:"There is nothing wrong with the split screen experiment, only its interpretation" Your words. So what interpretation convinces you that particles exist ?
The classical double slit experiment itself shows that electrons exist as particles as cathode ray tube behavior already strongly suggested. When electrons are projected toward the slits—and single electrons can be projected now—they pass through and register on the screen on the other side as points. Only when a large number have accumulated does an interference pattern start to emerge. Unless you make the source produce electrons of the same energy, the pattern will not be sharp, but it can be improved by using a more coherent source.
It's not the particle manifestation of electrons that needs interpretation, it's the wave manifestation—the interference pattern that emerges in the double slit experiment. de Broglie proposed that all matter has a wave nature, although it is not ordinarily observed. He derived an equation
pλ = h
where p is the momentum, λ the wavelength, and
h is Planck's constant. It follows that anything with large momentum would have a very small wavelength. For objects on the ordinary scale wave phenomena would not be noticeable, but for very small particles the wave nature becomes significant as the double slit experiment shows. In fact the interference pattern of the double slit experiment has been demonstrated for large particles and even for large molecules. (It may be that even the photon has mass. It would be very small.) David Bohm extended de Broglie's idea and others have followed. I cannot judge whether it is right or not, but I understand there has been experimental evidence in favor of de Broglie's hypothesis.