You know what might work is just buying an external capture card, and then modifying that. Like stripping it of it's plastic and safely mount it in your xbox. There are external capture devices that are USB and are about the size of a thumb drive for a fairly low price (not including shipping). Though for quality, it wouldn't hurt to spend a little more.
Here is some information for you that might help you find the right capture card for the job:
Inexpensive, Simple, Easy To Use, Low Quality VideoAVerMedia Capture Device $49.99 + $4.99 S&H = $54.98 TotalLight, Extremely Compact, Fair Quality Video, Reasonably PricedLifeView TV Walker Lite $72.00 + $2.50 S&H = $74.50 Total*Dimensions: 111mm(L) x 50mm(W) x 10mm(H)
*Mass: 88 gReliable, Normal Quality Video, Includes Editing Software Pinnacal DVC Dazzle 90 $72.00 + $4.99 S&H = $76.99 TotalVery Reliable, Extremely High Quality Video, Includes Editing Software Pinnacal DVC Dazzle 150 $124.00 + $4.99 S&H = $128.99 TotalI'm not sure if you'll be able to fit these, the
LifeView TV Walker Lite would be your best bet to fit it INSIDE your xbox, but, even that might be a bit of a stretch. If you wanted you could just make a mount and put it somewhere on the back of the xbox if you want quality video but can't fit the capture card inside your xbox.
Also, I'm not sure if these would work INSIDE your xbox, I'm just supplying you with a small list of cards ranging in prices and quality. You might get it to work in your xbox if you had it mounted like some people have their mini-HUB's mounted (so the places you put the cables are in the back of the xbox along with power/ethernet/video&audio.
Like I said, I'm not completely sure if ANY capture card will work INSIDE your xbox because you NEED a computer to do what you want with the capture card (record video, duh!). It's up to you.
Newegg.com is a great site to get different video capture devices in case you don't like the ones I've provided for you for cheap. They ship fast and are reliable. I hope I've helped you one way or another, if you need more information... OHH!! My knowlage ends here, I don't know what else to tell ya. If this hasn't helped you, then you're just screwed. Good luck!