I have to apologize. This is the second time I've recommended this board and I just noticed that it does not seem to have a composite input. I used it around 3-5 years ago with RGB inputs and separate sync (to which I had to add a sync separator chip).
But I have output my 8596E NTSC video to a Panasonic 5" BW pro video monitor and it gave a nice little image. Yet the same signal input to Sony professional monitors was unable to produce a good picture.
I think your scope images sum up the reason for this.
What you may want to consider is to strip off the sync, change the timing of it, then recombine with the video. The alternative is to "play", and I do mean play, with some of the composite video to flat panel controller boards.
I've been thru several of those and non were shining stars