The best way to prevent accidental cheating is to let players puzzle it out with new pieces as long as they remember which ones are new, but lock everything in once the round ends.
The next round, they can do the same thing.
This is also how we do it when I play my copy of this game. Also we allow players to put items up at the feast table before the Feast phase in order to "make sure" they have things set aside for feeding. But they don't have to actually discard the goods until the 'Feasting' phase comes up -- so if they want to make changes before then, it's also fine by us.