BTW, what's the reason for setting FPS override to a low value? Do you need long exposures?
If the camera frame rate is a few times higher than the projector frame rate, I don't expect any sync issues (there will be some jitter from the mismatched clocks, but as long as the projector is not advancing, it should be fine). Otherwise, if the two frame rates are close, but not identical, I expect trouble because the clocks will drift; the half-shutter trigger is not genlock (it does not affect LiveView frame timing - it simply saves whatever it finds in buffer).
A closer look at the footage shows the motion blur is, in many cases, at the top of the frame or on the entire frame, but never just at the bottom. The frame is captured from top to bottom, with rolling shutter - that suggests the defective frames were captured too early. The issue is clock drift, from what I can tell - try a higher frame rate setting for LiveView. The output frame rate will be driven by your external clock (so the data rate won't change), but the jitter will be a lot lower when LiveView is sampled at some high frame rate.
As a starting point, try running the projector at 1 FPS, LiveView at 30 FPS and give the sync signal in the middle of the interval where the film is not advancing. Once that is working fine, increase the speed and see how far you can push it, fine-tuning the settings and the timings. If you need more speed, try 1080p45 or 1920x800 60p.
For high speed scanning (with both projector and LiveView running at similar frame rates, doesn't matter if 1, 5, 10, 20, 30, 60 fps or whatever), you need genlock. Or mechanical shutter while the film is advancing.
