I'm with everyone else on the wand thing. It would have been simple enough to have him drop it. One narrative explanation for getting the wand back into Harry's hand would have been V asking for a demonstration of PT after Harry told him of it. Another would be to throw away the simplest timeline thing and let time-turned Harry come to the rescue with that solution, wand, cloak, etc. in hand. Though I don't know why V left him an hour on the time-turner either.

But:

My real confusion starts way before all of this. You have the idiot-child of prophesied destruction, and what you do not do is back him into a corner where he may decide to do something desperate. Making Harry feel threatened was a big risk to take with that prophecy.

V transforms into a super scary villain, putting Harry under massive duress, the exact kind of thing that would possibly cause him to destroy the world through time paradox or some other unknown power. It would have made more sense to bind him with an unbreakable vow long before then, to maintain the pretense of friendship throughout. So he guessed you're Voldemort, fine. Come clean, acknowledge what your plan to rule Britain was, and that you have been planning to place Harry as the ruler this time. Have that discussion. Come clean about the existence of a prophecy. Tell him you intend to resurrect Hermione. That you need to know what secret power he has so you can help him avoid the inadvertent destruction of the entire universe. Remind him of the centaur prophecy. Get him on your side that he is a serious risk to everyone. Brief the Death Eaters ahead of time, have a few that Harry doesn't know present out of uniform for a fake ritual of divination that supposedly requires him to be completely nude and holding no objects. At the agreed upon time in the ritual they all just AK him and Harry dies with his eyes wide going "Wait, WHAT?" and thinking you were his friend until the last.

V broadcasts his betrayal so far in advance, and that seems downright unsafe given what is at stake and what a giant question mark this boy is. You underestimate a 1st year, sure. But you don't underestimate a 1st year who is prophesied to destroy the stars and you, who you know has unknown powers.

I'm not hating though, EY. You're writing the story, not me. I know it's taken a lot of effort and I've enjoyed it immensely and I thank you for taking all of this time to write what has essentially been a free novel for all of us to consume and form a community around. I don't usually even think that hard about the fiction I read, but your story invites me to do so. It's been a great experience and I look forward to the finish.