TL/DR: Where can I find more information about building a GCC 4.7.0 cross-compiling toolchain for ARM (gnueabi) platform (intended to run on
I couldn't find a 4.7 gcc, only a 4.6. For information, I compiled the Pi's kernel on a fairly old Ubuntu machine (1Ghz, 768MB RAM) following the guidelines on this page: Kernel compilation
The build took about 90 minutes, compared to the 6 hours it is suggested that it would take on the Pi. The kernel runs fine on the Pi. Perhaps you can adapt these guidelines for cross-compiling other projects on your x86 Linux machine.