I think the obvious solution is basically this, with a Time-Turning involved. The troll could be real, or not (probably is). The hardest part about changing the past is faking the evidence including memories, but with a False-Memory Charm that becomes trivial. Memory charm Harry and possibly Dumbledore as well, depending on whether he objects "but I remember feeling a student die." They won't do it this way because it's too finger snap-ish and not dramatic enough, but if it's not at least addressed then I will allege a holding of the Idiot Ball.

Harry will need the help of Dumbledore or Quirrel to unlock the time-turner and cast the memory charms. Quirrel wouldn't help but I'd be interested to see his excuse; Dumbledore should be possible to convince but might not be. McGonagall or someone might be capable of it but wouldn't obliviate Albus without him asking for it. Unless this is what was foreshadowed with the question about her first loyalty?