"Can they at least make really, really sure that I am really, really dead before they do anything?"

That's my view, Joe, whatever bits they want to take, which is why I don't have a donor card and if they introduce an opt out system instead of opting in, I am going to opt out. I would rather trust my family to make sure I am dead, and then they can give the go-ahead if they choose to.
I heard a discussion about what happens when organs are taken, and what they do is check your (lack of) brain function and then keep your body alive by machine until they take the organs.
As far as I am concerned, if I am being kept alive, then I am alive.