I've still got an old TV that has SCART, so I use the component cable with a simple component to SCART converter. If you don't have that have you tried using the Aerial out and plugging that straight into the back of the TV? (I don't know if that will work, but it'd be worth a shot)
On my Gamecube I use a CARBY digital converter which outputs HDMI. Maybe there is something similar for the SNES?