It looks like the converter box could be the culprit. When I run the NTSC box into it, not only is the picture more stable, but I don't see the dot pattern.
https://youtu.be/ujVDmaDpexY
https://youtu.be/U_wqz0QPc0k
Broadcast signal, once the converter box was moved away from the isolation transformer:
https://www.youtube.com/watch?v=g5vzneETsGc
https://www.youtube.com/watch?v=oIIx9Rzd29g