My son's Kindle Keyboard 3G is now working reasonably well with a cheap screen from china. It didn't have the chip on the cable, so I knew it wasn't going to be perfect, but it was very cheap. I was careful to not disconnect the battery, thanks to
montalex's post, so whatever was loaded from the old screen is still there. I've also kept the old ribbon cable in case i need it for future repairs.
There's a little ghosting, but it's perfectly useable. Perhaps one day I'll pick up a proper Kindle screen and fix it properly, thanks to the really useful info in this thread. Thanks all!