Jefferson was the primary hand in writing the DoI. I am currently in the middle of reading American Sphinx which talks about the DoI to a certain extent.

When talking about the Declaration, its critical to understand that it's main thrust was written by Jefferson. So to understand its influence we have to understand what influenced Jefferson

So what did influence the young Jefferson?

A number of things. For example we find that George Mason, in his contribution to the writing of Virginia's state constitution said essentially the same thing that Jefferson says in the DoI at the beginning. Jefferson was keeping abreast of developments in VA so he certainly knew about that.

But Jefferson, like most if not all the Founders, was heavily influenced by the Enlightenment as well. But specifically, Jefferson utilized John Locke's Second Treatise when writing the Declaration. That is to say, the idea that people are born with certain right and have a right to overthrow their governments when these rights are threatened is a Lockean idea.

Finally, Jefferson, who was an excellent writer (but apparently not a great speaker) also studied several of his own writings, so that he could collect his ideas into a comprehensive writing.

Finally the DoI was influenced by other hands in the Congress who were sensitive to issues like slavery, and chose to alter those passages somewhat. The final result is distinctly Jeffersonian with ideas taken from Locke primarily, and alterations made by the Congress (some grammatical, some political).

Now that does not rule out the Act of Abjuration. However, history is tricky business. You could, if you want, argue that placement of certain animals and plants favored Europeans over the Natives, leading to colonization and allowing for a white, European America to be born. But of course no one argues that because the timeframe is too long. As you draw out the timeline, it becomes less clear how influential certain things are, because almost everything becomes influential. So could you say that the Act of Abjuration influenced Jefferson? Sure I guess so; Im unclear how aware of it he was.

But in asking what he was primarily drawing from to write the Declaration, its clear that Locke was the man. He may have known about the history (Jefferson went as far back as the Norman invasion of 1066 to blame England for suppressing freedom) but in reality, it's the Enlightenment, and Locke specifically, that are the key philosophical turning point of the Revolution.

Also, Jefferson does refer to expatriation in earlier writings. It appears that he felt that early colonists, in leaving England, had established a separate government entirely. This is somewhat akin to what you are asking, though it only goes as far back as the early 17th century, not the 1580s.