Dumbledore's plans and preparations look stupider the more I think of him. Transferring the sword was a big deal because the sword had a visible place in the headmaster's office, so he went into the trouble of making a fake (or getting Severus to do so) and then waiting for Phineas to learn of Harry's location and all that. But in 6th year, why didn't he get Harry to take him down to the Chamber of Secrets and find the basilisk fang? After the Horcrux lesson he could tell Harry what the fang was good for and to carry it around.