Sorry for bumping an old thread, but I had this exact same problem - noise when monitors connected, noise reacted to movement on screen.
I fixed it today, and my fix was not mentioned in this thread or others. My problem was, I had connected an unbalanced audio jack to a balanced output in the card. My original cable was a two-pole, standard patch cable.
I bought a balanced jack → XLR cable and connected the monitors with these, and the problem was fixed!
Anyways figured I’d leave a comment here for future reference.