First, a warm welcome, jjones! Glad to see you here.
This has been examined many times on this forum. However, let me address two things you state:
The number “1914″ is a number derived from subtracting 606/607 from 2,520. That number is: 1914 lunar calendar years that were remaining till expiration when the Common Era calendar came into use.
It's also derived from adding 2,520 to 607 + 1 for the zero year.
According to the calendar used in the Bible, that “1914″ is equal to 1914 times 360 days; which is equal to 689,040 days.
We're not so concerned with how many days in 1914 years. We are, however with 2520 years, which amounts to 907,200 days.
This forum has many times pointed out the difference between the lunar years used in Bible times and solar years used in the Gregorian calendar. You are right, the math is off, but some of your premises aren't quite correct. The deviation would be with 2520 years as 360 days vs. 365 days (907,200 days vs 919,800 days), a difference of 12,600 days, or -34.52 years. This would place the end of the 2520 years, if using the 360 day calendar at (1914 - 34.52), or 1879.48. I'm sure my math is off somewhere, too, even though I've been through this same calculation about a dozen times in the past year.
That said, the entire thing rests on two major assumptions:
1. That Daniel 4 actually is a dual prophecy. There is no indication in Daniel 4 that it is. Actually, Daniel 4:33 says it was fulfilled: "At that moment the word was fulfilled on Neb·u·chad·nez′zar." Done. No indication of a future prophecy.
2. That Jesus was referring to the destruction of Jerusalem in 607 (a hotly disputed date) in Luke 21:24. This is problematic, not only because of the date, but because Jesus used the phrase "Jerusalem will be trodden down". The Greek word is estai (Strong's 1510) and is in the FUTURE tense. He could not have been referring to an event that occured some 600 years in the past from when he stated it. http://biblehub.com/text/luke/21-24.htm
So, where did this come from? History shows the 2,520 years prophecy was adopted by Russell from Adventists, who adopted it from the Millerites. The teaching is not unique to JWs, but JWs took it to a whole new level. It's sad that they stick to this since it can be easily disproven multiple ways.