You'd really have to want some hot, steamy composite action to go through all of that nonsense. Instead, I'd convert the component to VGA, and then back to component and then back to VGA, then to S-video, then to RF, then to component, then digitized and compressed with a real time MPEG2 compressor set on low, then to VGA, then to a super long s-video cable which run across a busy street being run over by cars and then to 50AWG composite cable without any shielding which runs back across the street and into my window and to my TV.
But even after all that, you'll still have a li'l box with the PSP video that doesn't take up your whole screen.