Thanks all for comments. It has been a very interesting academic exercise for me.
That Alan Feuerbacher article is excellent. It gives a lot of the background and history of that date. Just listing a few points that relate back to my OP:
It shows why 536 BC (not 538 BC) was chosen; because it tied in with Balbour's Millerite date of 1873 AD and associated "synchronisms". It also seems to indicate that some Adventists were writing to Balbour and Russell as early as the late 1870's pointing out the error. Balbour and Russell falsely claimed Ptolomy's calendar supported their date.
The Gentile Times beginning in around 606 BC (or 604 BC) does have its origins with John Aquila Brown. Equating 606 BC with BOTH the start of the Gentile Times and the date of the fall of Jerusalem seems to have been sloppy writing that slipped in, in around the late 1870's.
Feuerbacher goes on to describe the steps taken by Watchtower to paper over the various problems. The shameless intellectual dishonesty of Watchtower knows no bounds!
Putting aside the intellectual analysis, it is breathtaking to think of how many lives have been wasted, how many families broken and how many lives needlessly lost (through lack of blood), over such sloppily put together numerology, made worse by a deliberate and concerted attempt to paper over its flaws.