Voldemort has reason not to do this, as it made a fool out of one of his tools and weakened his side by making them less willing to strike indiscriminately.

I disagree. The last part is an inference, and I think we have more evidence that the killing prevented any peace between Lucius and Dumbledore in Voldemort's absence.

(I don't know how much stress to put on this, but we learn that Draco thinks the death had this effect in the same chapter where he tells us to understand strange plots by looking at the outcomes. Seems at least 90% certain the author meant us to suspect Voldemort when he wrote that.)

Now, Donny just pointed out that Voldemort could have faked his death entirely by, say, transfiguring some chickens and burning them. We also know that his treatment of Bellatrix ensured her devotion to him would not count as a happy memory and would thus continue in Azkaban. I think he intended this effect, meaning he planned for the possibility of seeming to lose. It sounds like he planned for that from the start.

Setting fire to a chicken back in Chapter 17 should increase P(Dumbledore did it, and is a sadist). But supposedly DD's weakness lies in doing evil "For the Greater Good," not in having fond memories of the time he burned a woman to death. Seems more likely to me that he suspects Voldemort faked a burned body (per Donny's guess), but can't say so because he has no convincing explanation for why V hasn't visibly acted since then. So he just taught Harry to doubt such appearances.