I'd like to modify the LiveCD to boot with the NVidia binary drivers. Any ideas of how that might be done? I've tried several approaches, even a manual installation of the NVidia installer in a chrooted filesystem, but no success so far.
Create a Live USB instead of a Live CD. Ubuntu's Startup Disk Creator application will let you do this, and it allows you to save data as well as a persistent storage medium. You will need to load the ISO onto the USB and run it, install the NVidia drivers and you can then reuse it. It effectively becomes a portalable Ubuntu.
Here are some instructions on the Ubuntu Help website: