Is this not a pvp oriented rp, just as the show was? Having a team-based scenario would break the game, and while letting us make alternate characters who are antagonistic remedies it slightly, the problem still stand that whomever is playing the enemy would still be able to read the entries of the other "team" just by those entries being posted in the thread.

I think the GM should handle all entry-making, so that players can't control their futures any more than characters in the anime could. The GM should send private messages to the players depicting their entries, and players can use private messages to discreetly show each other their entries so that players who own characters that can't see the entry won't see it.