Update: I think I have solved some of the confusion. I recently did a test with 4 different Super Nintendo consoles, power supplies, and cords. Here are my results. I *only* get the scanning static lines if both the AV cords and power supply are 3rd party. If I mix an OEM AV cable with a third party AC adapter, no problem. Same thing is true if I use a third party AV cable plus original power supply... again, no problem.
So! The problem seems to be that using BOTH third part av cable and ac adapter is the issue. This sort of sucks, as I have recently been fixing up Super Nintendos, raising them from the dead. And when I get "broken" consoles, they never have the OEM cables or power supply. I don't want to give these perfectly functional SNES consoles to people with the static issue. And trust me, I know it's nothing wrong with the SNES consoles as they are ALL perfectly fine with OEM cables.
So, now since I am not rabidly against *just* the third party AC adapters, I am now open to using them, but need compatible AV cables.
So, I am wondering if anyone here has ordered third-party cables and does not have the static / rolling lines problem? And do you remember where you bought them if you did so online? I'd like to find a good combo of third-party cables that don't have this static issue.