I am no expert in physics but intuitive.
I think we are looking at the wrong thing to explain the interference pattern.
It is not the electrons that are of interest to study.
It is the matter/perhaps yet unknown particles the electrons travel trough.
The electrons creates a wave pattern in the matter around it. With each particle shot a new wave is created. These waves created roads where the waves take eachother out. The electrons slide trough these roads.
Perhaps when the electron hits the wall on which the pattern is detected creates some kind of push back to the media trough which it travels which leads to i sideway push to left and right scattering the incoming electrons sideways as well.