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.
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.