Other than that, my only other suggestion is to try the official HiDef pack for the video output from the XBox.
I don't think there's a difference. I have both, and the Monster has a better picture (very minor difference, but it's there) ... it's likely due to the breakout box design of the HiDef cables.
As far as your problem with the splitscreen is concerned, I'd suggest (while in the dashboard) to hold down both triggers and press in the two joysticks. this will force the display into 480p mode, as your component in may not accept interlaced signal.
To clarify : There are 4 modes we're talking about.
480i (480 lines, interlaced) - 240 lines drawn per frame - standard output
480p (480 lines, progressive scan) - 480 lines drawn per frame - better output, DVD progressive scan uses this.
720p (720 lines, progressive scan) - 720 lines drawn per frame - HDTV signal, 24bit color, 60fps, is well implemented for sports broadcasts due to the higher framerate.
1080i - (1080 lines interlaced) - 540 lines drawn per frame - 32bit color, 30 frames per second. Both 1080i and 720p use the same bandwidth, where 1080i has a higher resolution but is interlaced and refreshes slower, the color depth is better.
I personally prefer 720p to 1080i display. Amped2 and Xmen Legends are two very well done HD games.