the problem is the converter box.
whenever you convert a signal (an analog signal) to some other format, you lose information.
you need to find a way to pipe your video directly to the monitor... either by feeding it into an acceptably high quality input (VGA or component video (even s-video is not bad)), or by tapping RGB directly from the videocard into the video amplifier, which isn't easy to do.
composite input is about the crappiest input you can use next to RF input. s-video is only slightly better, but better than composite none the less.