It may be best to hand over the time turner but you do so after having a chance to think it through. Time turner. Plan. Decide that it is better to hand over the device for now. Write your analysis down. Give it to yourself at the appropriate time. (And give it to yourself again to make the loop stable.)
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; there isn't any meta-time (or at least, we've seen nothing to suggest such). If he were going to use the time turner to give himself advice, he would have already gotten the advice. And having used the time-turner right there and visibly, he couldn't use it "later not use it there" and have his going back in time undetectable.
A possible way he could use the time turner to help himself in this case would be to ask to go to the bathroom or somesuch, use the time turner, use the extra time to think, and then return to the room shortly after he left having thought about things.
(Edit: But this would be pretty obvious, and McGonagall probably wouldn't let him leave the room with the time turner in any case.)
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...
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.