Considering that he was winning the war before making his untimely exit in the early 80s, this strategy seems overly complicated.
On the other hand, he doesn't currently have much in the way to offer potential kidnappers.
...unless a family member of someone locked up in Azkaban takes him at his word that he's capable of destroying the place. I'm not sure Harry would pause even as long as he did for Hermione if that was the price demanded for the safe return of his adoptive parents. The narrative demands of the story make that unlikely, though.
In theory, the groundhog day attack could be only indirectly related to current events. The obsessive paranoia could merely be a side-effect of H&C trying to gain information, and the botched duel an unforeseen consequence.
I don't actually think that's the case, but it's a plausible enough scenario.
So add some sort of minor fear charm to that page of the textbook. Wizards aren't limited to paper and ink in their tools at conveying information to an audience.
Also, I'm pretty sure Harry has succeeded in terrifying Lucius enough that the latter isn't going to try pushing his luck too far.
But that is such a vague question. I could go on for hours about entirely irrelevant observations I wouldn't want to get out in public - how I feel about people at work, how much I enjoy certain bodily functions, sexual kinks. Nothing I'd want to tell them, but stuff I would objectively prefer for them to know than that I'd committed a heinous murder.
There's a lot of stuff in the fic that's explained only indirectly, leaving the reader to infer the truth - the Pioneer Plaque horcrux; Malfoy's belief that Harry is Voldemort; that Dumbledore is partially responsible for the potion that cleared up Petunia's appearance; the solution to Rita Skeeter's mistaken evidence (though that was made explicit recently); Skeeter's death; the self-serving nature of Quirrell's "strengthening" of Harry (learning to lose, inability to testify under veritaserum, rescuing a former minion, etc); the list goes on...
Given the number of people struggling with the "Azkaban Saturday" timeline, I thought I'd have a go at mapping it out and uploading the result to Google Documents. If anyone's got any corrections, feel free to say so.
On the other hand, it surely wouldn't be beyond the Dark Lord to come up with a system that accomplished all that without leaving such an obvious identifier on his minions.