I finally got it to work...
You want to hear the crazy method?
Everytime the installation stalls because it cannot read the disc, eject the disc and put it back in until it reads it. Every time the "can't find data.cab" thing comes up, eject the disc, throw in the PREVIOUS disc, wait for the error message, throw the right disc back in, and it should work.
That's what I did. It's far from scientific, and it's far from a logical outcome, so don't be surprised if it doesn't work for you.