I have one problem with the snake being a horcrux. SHe is with Voldemort when he first appears in GOF. Why couldn't he "resurrect" himself at that point if one of the horcruxes was readily available?
LV didn't really have much of a body then. I don't think it would have done him much good. He didn't get a body back until the end of GOF.
I think Dumbledore explained the Dark Lord using Harry as he wanted to use Harry's blood to break one of the protection spells on him. Plus, he was going to kill Harry and didn't expect to survive. Maybe he didn't want to "waste" a Horcrux, since the plan was for there to be no surviving witnesses to his coming back. He also wanted to call his death eaters to witness his destroying of Harry to prove to them he was back and call them to see who was still loyal. Also, Voldemort doesn't know that Dumbeldore or Harry knows that he even has Horcruxes, let alone that any have been destroyed.
I am not sure that the snake is a Horcrux, doesn't Dumbledore say that he isn't sure, it is a hunch? Maybe since Voldemort used the diary and it got destroyed, he didn't want to attempt to use a Horcrux and have anything go wrong again.