Nearly all of the algorithms I described extend well into multiple dimensions. I'm not sure how Eller's would work in 3D, but there is probably a way. And the Binary Tree and Sidewinder algorithms seem like they ought to be possible to adapt to 3D, but I don't immediately see how. The others, though, are all trivially expandable to n-dimensions (just add "up", "down" and any other directions you like to the list of possible moves).