The rationale is that I'm wondering if there might be something odd happening when composite gets transcoded to component, and since you have no other sources that start out as component there's no drawback to operating that way (it's actually a "purer" approach). If the behavior remains when you remove the composite-to-component transcoding process, that will suggest something odd about the composite output. S-video could also be used, but there is still a transcoding step involved so it's not as definitive a test.

There is no need to buy a cable - just use one of the three connectors from the component cable. It's the same kind of cable.