With the region set to NTSC M and the console hooked up via component, I can enable 480p or even 720p (not that I need to go that far!) and it all seems to run just fine. There are faint diagonal lines going on in scenes with large blocks of colour, but unless there’s an easy fix for that, I’m not massively bothered by it. ?
My assumption would be that the diagonal lines are likely interference due to low-quality cabling.
Unfortunately, good-quality Xbox component cables are hard to come by, but you have a few options. You can track down either the High-Definition AV Pack* or the Monster Cable equivalent, both of which support digital audio; or you can try emailing RetroGamingCables.co.uk to see if they would be willing to build you a component cable. (Sadly, Retro-Access.com doesn’t have any Xbox cables, and I’m not sure HD Retrovision has anything planned for the original Xbox.)
* This is the official Microsoft breakout box, which has outputs for YPbPr component, analog stereo audio over RCA, and digital stereo/surround audio via TOSLINK. You might be able to find one with the original cables, but, if not, you can always just get a good, shielded 5x male RCA to male RCA component AV cable; and be sure to inspect the photos before buying–I came across one seller on eBay who was selling one with a connector that had started to rust.