You seem to misunderstand how the time-turner works (or at least, how it's been suggested it works). You don't get to overwrite anything; the universe doesn't "end up in" a stable state that results from using it
My interpretation of the "DO NOT MESS WITH TIME" incident was that you can try setting things up so that temporal consistency implies the result you want, but actually ruling out every other possibility whatever, including vast classes of outcomes you never even imagined, is next to impossible, at least for an 11-year-old boy, however smart. It hadn't even occurred to him that there was a problem in his reasoning when he tried the experiment that gave him "the scariest result ever in the history of science". Temporal consistency in the presence of time loops is another blind idiot god, far more swift and powerful than evolution.
Anyway, he still has the Time-Turner. All that stands between him and it is a magical lock. How difficult can that be for him to get around? No, actually what stands between him and it is the author's necessity not to unbalance the plot by giving him a get-out-of-jail-free card.
Harry's error in the experiment was responding to "DO NOT MESS WITH TIME" with the same. If he didn't have the property of responding to that message with the same, that message wouldn't appear.
Actually, this whole consistency-based time travel seems to be an extremely expressive thought experiment infrastructure for thinking about Newcomb-like problems and decision theories able to deal with them. Maybe I should do a top-level post on that (I don't have a sufficiently clear picture of the setting, so I might be wrong about its potential)... Though I consider that happening unlikely, so other people who understand UDT are welcome to try.
Update: Please post new comments in the latest HPMOR discussion thread, now in the discussion section, since this thread and its first few successors have grown unwieldy (direct links: two, three, four, five, six, seven).
As many of you already know, Eliezer Yudkowsky is writing a Harry Potter fanfic, Harry Potter and the Methods of Rationality, starring a rationalist Harry Potter with ambitions to transform the world by bringing the rationalist/scientific method to magic. But of course a more powerful Potter requires a more challenging wizarding world, and ... well, you can see for yourself how that plays out.
This thread is for discussion of anything related to the story, including insights, confusions, questions, speculation, jokes, discussion of rationality issues raised in the story, attempts at fanfic spinoffs, comments about related fanfictions, and meta-discussion about the fact that Eliezer Yudkowsky is writing Harry Potter fan-fiction (presumably as a means of raising the sanity waterline).
I'm making this a top-level post to create a centralized location for that discussion, since I'm guessing people have things to say (I know I do) and there isn't a great place to put them. fanfiction.net has a different set of users (plus no threading or karma), the main discussion here has been in an old open thread which has petered out and is already near the unwieldy size that would call for a top-level post, and we've had discussions come up in a few other places. So let's have that discussion here.
Comments here will obviously be full of spoilers, and I don't think it makes sense to rot13 the whole thread, so consider this a spoiler warning: this thread contains unrot13'd spoilers for Harry Potter and the Methods of Rationality up to the current chapter and for the original Harry Potter series. Please continue to use rot13 for spoilers to other works of fiction, or if you have insider knowledge of future chapters of Harry Potter and the Methods of Rationality.
A suggestion: mention at the top of your comment which chapter you're commenting on, or what chapter you're up to, so that people can understand the context of your comment even after more chapters have been posted. This can also help people avoid reading spoilers for a new chapter before they realize that there is a new chapter.