Well, actually, because of the unique way we update the hack, it's entirely possible to do an LP of LC right now. You start with the current version of the live beta, which offers access up to the first island of the Orange Islands and play away. When you want to update, you keep your existing save, and simply patch the newly updated patch onto a clean rom, and then resume. We made a concious decision after releasing beta 3.2 to ensure that it was possible to complete the game without having to restart ever again.
Normally, the reason you have to restart after a new beta is because variables have changed, maps have changed, etc, and that necessitates a restart. The difference is, we're quite far through the hack, and everything before the OI is completely set in stone (bug fixes aside).