So, this looks like more on the theme of V leaving some trace of himself on Harry's psyche.

So agreed. I've been over that one line often.

I'm not sure what he hopes to gain by showing all this to Harry, though... how does it get him any closer to killing him (assuming that's the goal)?

Right, I think he did it to keep suspicion on Hagrid again, in hopes no one would figure out the truth.