Gigantopithecus or Paranthropus? Cryptomundo

What fossil candidate fits best with the reportedly upright, hairy, 6 feet to 8.5 feet tall forest giants of North America? Everyone seems to favor Gigantopithecus, but what of the other major fossil choice, Paranthropus? See also, It Starts With Animals and Cryptozoologists and ghost hunters gather in Watertown, MA.