"It was time to leave this shack and take charge, with a wand that would now do his full bidding."I never thought that meant anything other than that Voldemort took Snape's wand, thinking Snape's wand was now the Elder Wand. And, yes, that that meant the wand Voldemort was using from that point on was Snape's wand. Since I was wrong in that, do we know what happened to Snape's wand?
I still like the idea that Draco Malfoy was wandering around with this powerful wand all that time and didn't know it, because he's, y'know, Draco Malfoy. And that Harry took the wand from him and therefore took possession of the Elder Wand but didn't know what he had for a while either--that's what I had got from the line "who had come to take full possession of it at last"--acknowledgement, true acceptance of what he held. It feels more satisfying than the idea that the Elder Wand's sitting in Voldemort's hand but realizes that somewhere far off Harry has simply nicked a non-significant wand out of Draco's grasp and that makes the Elder Wand shift allegiance. Not quite sure I'm buying it yet, though technically I can see how it works.
It does make more sense now that I'm told "elder" can be a kind of wood, which is a better argument that the wand is fixed. I assumed "Elder" as a title, in the sense of "elder brother"--first-come, first-ruling, oldest and most senior. The first time we hear the word is within The Tale of the Three Brothers: "So Death crossed to an elder tree on the banks of the river..." From the high-toned prose of the story I assumed that was poetic-speak for "ancient tree." But elder is short, it seems, for elderberry?