The development team has implemented a clever mechanism that loads the Balanced Brawl files from an SD card. You just have to download the files to a card (and remove all your saved custom Brawl stages), pop it in the system and launch the Stage Builder mode -- the loader will automatically take over from there. If you're interested in having a Balanced Brawl party, we suggest throwing one soon, before Nintendo releases a firmware update to block the unlicensed balancing act.
[Thanks, Kyle]