Excellent line of reasoning, Terry! I will have to try that one out. Of course, if you had asked me that question even 2 years ago I would have said, "Almost all of them."
After all I had read articles quoting reknowned secular authorities as setting the dates by JW standards. I "knew" 607 BC was right, whatever else might be wrong. I reasoned this way: Surely they would NEVER misquote or misrepresent secular authorities against which their words could be referenced and found to be false.
Rockhound's thread shows up my problem: Nebuchadnezzar NOT KING in 607 B.C.
If I were to ask my father, "Okay, show me any...any source that is non-Jehovah's Witness which represents 607 BC as the date for the destruction of Jerusalem." He would print off a quote from a publication that cited Grayson and work the math from there...ending in 607 BC!
Then the argument becomes whether Grayson actually says what the WTS implies that Grayson says. I did the math working from those quotes myself, to "confirm" that even secular scholars agreed with the WTS dates. I used to tell Bible Students that I knew for sure these dates were secularly confirmed on that basis. I helped perpetuate a lie. I don't have a copy of Assyrian and Babylonian Chronicles (1975) laying around the house.
On this issue the WTS brazenly, outrightly lies and deceives JWs by contextually presenting scholars as agreeing with their dates. It fooled me, not because I was gullible but because they betrayed a trust they created, they betrayed an obligation they laid on themselves to tell the truth.
Without some degree of trust, everyone would be required to become in expert in every field. So I don't think trust was, in itself, a bad thing—although it was misplaced as it turns out. But it is this trust that makes overcoming the lies so difficult.
I mean, even if the average did dig as deeply as the Appendix in the back of Let your kingdom come they would come away believe the Ptolemy canon was the most vital piece of evidence in defense of 586/587 BC and would have no clue as to the strength of evidence regarding 597 BC as the date for Jehoiachin's exile (which automatically eliminates 607 as a possible date for the destruction of Jerusalem).
Because they will view WTS sources as superior and more honest, they may cite secular works but it will most likely be the doctored citations from the Publishing Company at whose feet they worship. That is what I ran into trying to discuss this with my parents before my dad initiated a JC proceeding. On one occasion I asked whether it matters that the secular sources cited show different dates than the dates that appear in the articles. He said he wasn't going to get into a pointless debate over words.
If they trust the Society's authority, how do you show that trust to be misplaced? I really think the fine minds that post here (such as yours) can come up with methods for systematically proving that trust misplaced. The trust was instilled systematically, it seems reasonable that deconstructing it would need to be systematic as well.