Really helpful post.
I don't have access to the game atm, so I can't check, however I can't help but wonder about certain details explained here.
The main one being about having the Zenith Weapon equipped. Is this stated explicitly in the Quest Dialogue (again, I can't check atm)? If not, is this just an assumption? Has anyone gotten one while not having the Zenith equipped? I understand, at this point it's a "better safe than sorry" kind of thing, but until full experiments/testing have been done I'm skeptical of things. One of the main reasons I would really consider this is the point you made about not needing the shield equipped on PLD. It could just be coincidence, I understand that, but would be curious to see more hard evidence.
Also, I have found no organized attempts at a true drop rate calculation and/or whether or not certain FATE's have better odds. At this point, for the above point and this one, all I've seen are speculation but no hard data.
Please don't take this the wrong way, you have definitely provided a lot of helpful information here and I don't mean to detract from that, however I believe these are some points we should confirm fully to debunk any myths out there.