(EDIT: formatting)
The Obvious Solution: Avert Destruction at Every Possible Point of Intervention
Notice that the solution classes above are not mutually exclusive at the planning stage, and can even be combined with some as backups for others. Naturally, then, part of the lesson is to do exactly that - because Harry needs this to succeed.
To show that I can figure out exactly how to combine them and the details of how Harry should talk his way out of the box, I’m going to write out the combination as a hypothetical Chapter 114. Doing so requires me to pick specifics out of each solution class, but should get my point across.
Chapter 114: Final Exam Solution
Even as Voldemort was still hissing out his threats, Harry's mind started racing with wordless inferences.
Must at least evade immediate death - can't sort out how to deal with other problems if I'm dead -
- must also avoid unnecessary risk of destruction -
Voldemort had intended the Unbreakable Vow to compel no positive action in itself, nor to compel inaction in case of disasters already set in motion by Harry’s own actions. But being a knowing bystander to disaster, when he could have intervened, would be allowing it to happen by his own actions just as much as if he had set it in motion himself; Hermione would agree once she’d had everything explained and come to understand heroic responsibility.
There were catastrophes every day; 150 000 deaths a day could hardly be considered anything less. Hermione would want those lives saved, just like he would. And unless someone ended death, humanity (and life) would die out eventually. It was a statistical fact that those two different spirits could not exist in the same world.
Any vow was Unbreakable, if made by the right person.
- the Vow requires me to choose Light and world optimization, therefore my survival decreases the risk and expected severity of future disasters barring exceptions like self-sacrifice -
And now Harry couldn’t slow his thoughts down to put them in words, not even if he wanted to, not while his survival depended on thinking quickly; the Unbreakable Vow he had sworn was driving his best efforts as a rationalist towards the course of least destruction and he couldn’t stop it any more than an Artificial Intelligence could disobey its programming.
- he just said I have sixty seconds; how can I get out of this or at least stall for more time without drawing fire from the Death Eaters -
- spells requiring incantations or wand movements are out of the question, but free Transfiguration uses neither -
A wordless image of Transfiguring a cross-section through the troll’s brain flashed through his mind. To kill thirty-six Death Eaters at once, though, he’d need to pick a small but immediately fatal cross-section so that the total volume would stay small enough to affect quickly -
- sever the medulla oblongata and they die in a fifth of a second -
Free Transfiguration required his wand to be touching part of the volume he wanted to Transfigure, but there was no reason to limit partial Transfiguration to part of one object, not now that he’d put so much practice into seeing past the illusion of objects in order to perform partial Transfiguration in the first place. And while he could retest Transfiguring air now that he understood partial Transfiguration, he didn’t want to risk giving anything away by looking down near his wand.
- wands are robust to minor chemical burns -
Harry visualized a thin line (noticeably less than a millimeter thick) along the outside of his wand from the tip to his pinky finger, up his skin to his shoulder and then back down to his heel where it touched the bare ground. The line then split into thirty-six separate lines along the ground, one for each Death Eater, leading to their shoes, through their shoes and socks, and finally up their bodies to the desired cross-section of brain.
His conscientious Transfiguration practice had done him a great deal of good; not only could he hold the complex volume in mind while continuing to think, but his shaping practice would also let him Transfigure only the intended cross-sections into sulfuric acid without sustaining damage from routing the connecting line through his body. After getting those sections to Transfigure first, he would just cancel the Transfiguration rather than complete it. As further protection against damage, he also chose a target form with no changes to the material along the connecting lines, keeping the acid only where it would be needed.
He held the visualization of this Transfiguration in his mind, ready to perform it at a moment’s notice if it were needed, but didn’t cast the spell just yet.
- I have a plan now, but it involves thirty-six deaths and doesn’t buy me much time. Voldemort will use Muggle methods to kill me if he has to; at best I might be able to escape on Quirrell’s broomstick-bones and maybe grab the pouch and Stone while he’s distracted. -
Time to look for a better plan, or rather additional plans. Hermione would also consider Voldemort’s plan a massive catastrophe, and that was definitely aided by Harry being stupid. He hadn’t sufficiently questioned Quirrell, hadn’t kept the symbol of the Deathly Hallows a secret rather than showing it to Quirrell, hadn’t reconsidered telling McGonagall about the sense of doom, hadn’t told the Order what really happened in the Azkaban breakout, hadn’t declined the Azkaban breakout as a stupid idea, hadn’t realized something was wrong with the note before going back in time, too many mistakes to enumerate now...
...so now he had to keep planning to stop Voldemort, had to avert disaster at every possible point of intervention. And also improve his ability to continue averting disaster afterwards if he survived -
- besides just survival, self-improvement and acquiring more resources are also useful -
The terrible clarity continued to strengthen its grip on his mind, although it no longer felt Dark now that it had been harnessed this way. It felt... integrated, a set of skills that retained their chaining to each other but also blended smoothly into the rest of his mind.
(Somewhere in a distant back part of his mind, Harry noted just how much the Unbreakable Vow had altered his mind and made a note to restore pre-Vow Harry in a more optimized world, then let him choose how he wanted to live his life.)
Destroy Voldemort’s current body by Transfiguring part of the ground underneath him into antimatter: Would be a setback to him, but is also a self-sacrifice move. Hermione might survive to become a Light Lady if I keep the amount small enough. Keep the idea around in case self-sacrifice seems worth it later, but keep looking for more plans.
Cast a spell on Voldemort directly and hope the resonance kills him: Another self-sacrifice move, and will probably draw fire from the Death Eaters unless I make it a quick Transfiguration I can finish before the resonance gets me too. I have no assurance that doing so will kill him rather than just force him out of his current body. Keep looking.
Tell Voldemort some secrets that aren’t actually that useful: Largely failure. Stalls for time, but he’ll rapidly grow impatient.
Tell Voldemort some secrets that are useful: Also largely a failure. Better stall for time at the expense of adding to his future power and making him harder to stop later, and he’s probably still going to kill me.
Voldemort seems to have most of the immediate power here. For him to keep you alive, you’ll have to convince him that it’s in his best interests to do so. You must either find something you have that he wants, or find something you can do which he fears, and present it in such a way as not to immediately raise his guard against persuasion...
Ah.
Transfiguration options still at the ready, he began to hiss...
(remainder in child comment due to length limits)
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The big problem is that he left Harry his wand. If he uses more precautions against Harry, but still keeps leaving Harry his wand, then that makes the fact that he left Harry his wand less realistic, not more. So I actually think that you should go the other way with it - have him be less paranoid about Harry. Because otherwise you're making the inconsistency even worse. He's being cautious and paranoid enough to strip Harry's clothes from him, but leaves the wand in Harry's hand for one moment longer than he has to? It makes more sense if he has the Death Eaters throw a bunch of Finites at him to check for residual traps left by Dumbledore, and for that to be where he sees most of the threat coming from.
This.
Voldemort's not only being paranoid enough to strip Harry's clothes from him, he's being careful and cautious enough to remove an object Harry Transfigured without letting their magics interact. That kind of attitude is jarringly inconsistent with leaving Harry his wand for no apparent reason.
LukeASomers already suggested adding a reason for Harry to have his wand. I think that adding such a reason combined with changes that increase our estimate of Voldemort's estimate of P(Time will try to thwart Voldemort's attempt to avert the prophecy through something other than Harry | Time will try to thwart Voldemort's attempt to avert the prophecy) would make things seem much more consistent; leaving Harry his clothes and having some (not necessarily most) of the Death Eaters looking outwards would both help with the latter.
The reason I suggest increasing readers' estimates of Voldemort's estimate of P(Time will try to thwart Voldemort's attempt to avert the prophecy through something other than Harry | Time will try to thwart Voldemort's attempt to avert the prophecy) rather than just making Voldemort less paranoid overall in this situation is to avoid worsening the Villain Ball complaints; shifting his paranoia partly elsewhere allows him to be the sharp antagonist we're expecting while suggesting that he's confident the precautions he takes are sufficient to neutralize Harry as a threat (which allows Harry to win). That confidence isn't out of place for his character - even though he's read Muggle books, it's entirely plausible that he hasn't integrated that knowledge well enough to start questioning what he knows as the limits of magic (and thereby come to think of partial Transfiguration, or more generally realize that Harry might question those limits and succeed in discovering something he can wordlessly cast without pointing his wand).
The particular changes I mentioned also have the side benefit of not really affecting the major proposed solutions to the Final Exam. If you do change it, I think a historical version should be preserved for correspondence with the Collective Intelligence's effort.