The /clone command, if I understand correctly, copies the selected area with opposite corners (x1,y1,z1) and (x2,y2,z2) to the new area such that (x1,y1,z1) is moved to (x,y,z). However, even though the two areas are nowhere near each other, I'm still getting the "Source and destination cannot overlap" error message.
If it matters, the blocks I'm copying are Polished Andesite, Fence posts, wooden doors, stone pressure plates, stone brick stairs, and air.