I can't see the FB page either, but there are plenty of HDMI out tutorials that take advantage of a Component to HDMI converter. Here's a really popular post that gets referenced a lot: https://www.xbmc4xbox.org.uk/forum/viewtopic.php?f=13&t=1984
What this person has done is taken a Component to HDMI converter, removed it from its casing and made it an internal component in the Xbox by hardwiring it to the motherboard. OP of that thread never came through with a full tutorial though, so you'd have to reference the Xbox's AV pinout to figure out how to wire it up.