If Harry Potter already had the contract written before going into Gringotts, how did Moody’s eye not see it? I suppose it is possible that Moody’s eye cannot see into the folded space of Harry’s pouch, but Harry has no reason to assume as much, and is smart enough not to take the risk. And whether or not Moody can see into folded pouch-space, this line makes no sense at all: “Moody paused as his Eye caught sight of the second half of the document as Harry Potter slowly, as though reluctantly, began to unfold the top upward.” Moody’s eye can easily see through mere paper. Why would he be able to see only the unfolded portion of the document?
This chapter would make a lot more sense if Harry committed the wording of the contract to memory beforehand and wrote it down at the meeting, and if McGonagall or Dumbledore was escorting Harry, not Moody.
You are entirely correct. I mis-remembered the events of book four.