Did anyone else find it increasingly implausible that the teachers kept trying to speak to Harry while he was thinking? The first one or even two approaches made sense, but if a person who has just lost a close friend says that they want to be alone until dinner, the only sensible course of action seems to be to say "okay" and leave them alone. It'd be one thing if he hadn't spoken for anyone in a month, but this was just a few hours: it'd have been completely reasonable for anyone to want to be alone for that long.

Granted, given that this is Harry, they might have thought that he was in risk of doing something really rash... but if they feared that he'd do something so bad that it wouldn't have been enough for them to guard the door to the room where he was in, then McGonagall would have been insane to unlock his Time Turner! And if they thought that he was in danger of developing some really crazy plan while thinking, it should have been obvious after the first couple of times that interrupting him now would just make him more unreceptive, and it would have been better to wait until dinner.

I'm just drawing a complete blank here - why did they keep doing it? Doesn't seem to make any sense to me.

I wonder if Eliezer is just being cautious, trying to steer the story away from anything that people would dismiss as blatant cryonics propaganda, and instead just plant enough of a hint to get the normals reading HPMoR, how should I say it, emotionally interested in the idea that a freshly dead person might be preserved, and revived later when we know more.

Could you propose a specific way that a high-end biochemist can help with the condition in which Hermoine happen to be?