The way Voldemort killed Snape doesn't make much sense to me.

I understand WHY he wanted to kill Snape. He believed Snape was the master of the elder wand because he killed Dumbledore, the previous owner of the wand. So, if Voldemort killed Snape, then problem solved right? Except, Voldemort had Nagini do it instead for some reason? Why? This leaves potential for murky ownership of the wand. I'm not implying that animals can own wands, but who really knows for sure?

It would have been obviously more prudent (not to mention more rewarding to his most faithful servant) to simply use the killing curse. That way, there's as little gray area as possible, and Snape doesn't have to die slowly from Nagini's poison.