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Kindly comments on Harry Potter and the Methods of Rationality discussion thread, part 20, chapter 90 - Less Wrong Discussion
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Here's how I would have saved Hermione if I were Harry.
In an accessible but seldom visited hallway of Hogwarts, a rail-way sign reads 6PM to 5PM Express.
At 5:00, a boy materializes under the sign. He is wearing a rail-way conductor's hat. He is holding a trunk. His name is Harry Potter.
Conductor Harry puts down the trunk. He opens the lid. Inside his Trunk of Holding are wooden seats numbered 1 through 1000. All seats appear to be empty.
Conductor Harry yells "Arriving at 5PM! Please add one tally to your forearm now".
Silently, hundreds of people draw a tally mark on their arms.
Conductor Harry steps away from the trunk and the hundreds invisible passengers of the 6PM to 5PM Express disembark.
At 5:10, Conductor Harry closes the trunk lid. He stashes the trunk [EDIT] and Time-Turner in the Great Hall.
At 5:12, Conductor Harry burns his conductor hat. He draws one tally mark on his previously blank arm, and puts on his invisibility cloak. He sighs. He has a long day ahead of him.
...
At 5:30 in the Astronomy Tower, a smelly and disheveled Harry Potter pulls off his invisibility cloak. He is covered with hundreds of tally marks, and looks like he hasn't slept in days. He yells "Screw this, I'm done!", collapses on the floor, and falls asleep.
...
At 5:40, the original Harry goes to his room. He has done no time traveling today, and has no tally marks on his arm.
Original Harry locates his trunk and his conductor's hat.
At 5:45, Original Harry brings his trunk and hat to the hallway with a 6PM to 5PM Express sign.
At 5:50, Original Harry puts on his conductor's hat. Harry -- now Conductor Harry -- opens the trunk, steps aside, and yells "All aboard the 6PM to 5PM Express!. Please go to your assigned seat."
Hundreds of invisible Harrys silently climb into the trunk. Each Harry counts the tallies on his arm and sits in the corresponding seat.
At 5:59, conductor Harry yells "Last Call for the 6PM to 5PM Express!"
At 6:00, conductor Harry closes his trunk. He picks up his trunk, and flips his time-turner.
Using this method, Harry can get as much time as he wants to study obliviation, transfigure large objects, or anything else, all with a single twist of his time turner. That's more than enough time to learn to obliviate yourself (and maybe the Weasley) and fake Hermione's death.
Whether this method works or not is up to the GM; the as-stated rule is that "information cannot go back more than six hours in time, using any combination of Time-Turners", which would allow this, but it's possible that anything which results in someone having more than 30 hours to a day is also bad. Granted, the hypothesis that 6 hours is the universe simulator's buffer size would suggest that this works.
It's a bit scary that if this scheme fails, there's no clean way for it to fail. In the very simplest case -- you go back in time 6 hours and then try to go back in time 1 more hour -- presumably the Time-Turner just doesn't work and nothing happens. Here, that outcome is not self-consistent: there's only one spin of the Time-Turner, and if it fails then there are no multiple Harry Potters so there is no reason for it to fail.
So if this scheme goes against the Time-Turner constraints, the only consistent outcome is that something unspecified happens to one of the first 6 Harry Potters to prevent them from getting back into the trunk. And summoning unspecified obstacles by the power of Time-Turner consistency seems like a really bad idea.
To fix this, we could have each Harry Potter toss a 100-sided die and leave the loop on a 1 being rolled; then run this algorithm several times. It's likely that spontaneous catastrophic failure has a probability much less than 1%, so the most likely consistent loop assuming this scheme doesn't work is one in which Harry rolls a 1 early on, which is very unlikely to happen assuming this scheme does work. So if several trials of this algorithm consistently keep ending after 1-6 repetitions, then it's almost certain that the universe doesn't like it.