Simon said, "The 1914 date was something they plucked out of the air..."
Not entirely. If you add 40 years to 1874 you arrive at 1914. The "Bible Basis" for this was 40-days-for-years to allow for the sanctification of the tabernacle. Today there are certainly very few JWs who understand this detail of "Bible-based chronology".
The pivotal year 1874 is thus entombed in Watchtower doctrine.
"God has a set time for every feature of his plan, and that we are even now in this "Day of Vengeance," which is a period of forty years; that it began in October, 1874, and will end in October, 1914 [very shortly]." Studies In the Scriptures Series IV - The Day of Vengeance -pp.546, 547"