If it is a simulation, and time travel devices are limited in ways to save on computation and such, some of these restraints make sense: the quibble over what counts as information is resolved as "anything that will force the simulation to recalculate futures", the simulation buffer is locked to one per time-turner because allowing an arbitrary number of retries would cause the computation requirements to explode, and Harry can get around the limit by using someone else's "turn", even if they can't use it, because they have information that the simulation won't allow to travel.

My money is on Dumbledore's timeturner. McGonagall, Snape, and Amelia Bones won't suspect it, all having witnessed Dumbledore receive future information (therefore he can't travel back in time far enough). Harry will capitulate to Dumbledore's offer of the Timeturner once he determines that a) Dumbledore knows Harry was involved in the Azkaban break, and b) being able to travel the full 6 hours will convince the rest of the wizarding world, including his teachers, that Harry was not involved. Dumbledore will do this because it suits his interests (or sense of drama) to have war declared on Voldemort.