Two other points:
But I'm trying to keep this portion of my research as simple as possible
I strongly suggest you read The Gentile Times Reconsidered. It goes into depth and, frankly, it may be a nice idea to keep the research simple as possible, but it's only by going in depth you realise that Neo-Babylonian chronology is clearly established by physical evidence from that time period. Cuneiform tablets, the House of Egibi records and so on. You just can't argue with a picture painted by 10,000s of pieces of evidence.
Is it likely that both dates 587 & 607 have their own significance?
The seond point to grasp is that you need to go back to the beginning of this whole idea of when the Appointed Times of the nations begins (which is the whole reason we are skulking about 100s of years BCE).
Re-read Luke 21: 20-24:
20 “However, when you see Jerusalem surrounded by encamped armies, then know that the desolating of her has drawn near. 21 Then let those in Ju·de′a begin fleeing to the mountains, let those in the midst of her leave, and let those in the countryside not enter into her, 22 because these are days for meting out justice in order that all the things written may be fulfilled. 23 Woe to the pregnant women and those nursing a baby in those days! For there will be great distress on the land and wrath against this people. 24 And they will fall by the edge of the sword and be led captive into all the nations; and Jerusalem will be trampled on by the nations until the appointed times of the nations are fulfilled.
Everything in Luke 21: 20-24 is written in future tense (see in bold above). So Jesus, talking in 33CE, was talking of future events. There is nothing to suggest that the last part re Jerusalem had actually started hundreds of years before. If so Jesus would have said, "and Jerusalem is being trampled on by the nations...", or "and Jerusalem will continue to be trampled on by the nations...".
It's just an (old) interpretation of scripture that doesn't bare up to scrutiny, particularly given the future tense the whole passage was written in.