Don't take it from me, take it from Winston Churchill - 1776 was based upon 1688

He has repeatedly been voted the Greatest Ever Briton, and the very first of just 8 Honorary Citizens of the United States. He wrote this:

"The Declaration (of Independence) was in the main a restatement of the principles which had animated the Whig struggle against the later Stuarts and the English Revolution of 1688, and it now became the symbol and the rallying centre of the Patriot cause"

– from History of the English Speaking Peoples, Volume II (1956). The final chapter of Volume II is entitled 'The Revolution of 1688'; the first chapter of Volume III is entitled 'William of Orange'. It's brilliant stuff, and very far removed from the narrow Northern Ireland version of events.

He paints a scene of a pan-European alliance of Protestants / Calvinists and all mainstream Catholics, united against James II and Louis XIV. 

“Diverse interests and creeds united in a strategy far-seeing and broad-minded”

Churchill’s ancestor, Sir John Churchill, was one of the first group of nobles in SW England to defect/mutiny from James II in rebellion.

History goes full circle: Sir John Churchill joined a pan-European allied force which crossed English Channel to overthrow a tyrant in 1688. His descendant Winston Churchill co-led a pan-European (&US) allied force which crossed English Channel to overthrow a tyrant in 1940s.

..........

Here is another source about William's 1688 Declaration:

"...Having brought matters to a great forwardness, the Prince of Orange, to justify his under-taking to the world, published a Declaration divided into 26 articles, in which all the mischiefs and grievances of this unhappy Reign are particularly enumerated, and a redress proposed by a free Parliament; which Declaration, as it would give too great an interruption to the thread of the narrative, is omitted here, and placed at large in the Appendix, more especially as the matter of it is particularly set forth in the several parts of this life.

The said Declaration was ready to be sent over to England, with another of the same import to Scotland, when the Prince being informed, that K. James by granting most of the Bishops demands, and retracting many of the arbitrary and despotick actions he had assumed to exercise, had taken measures to render it ineffectual; and as the Partizans of K. James had industriously spread it abroad, that the Prince intended to conquer and enslave the nation, his Highness to obviate these new pretences caused 14 days after an addition to be made to it, shewing the imperfectness of the redress offered, since the King might resume at pleasure, what he then seemed willing to lay down, and that there could be no secure remedy but from a free Parliament; and arguing from the disposition of his forces, and the numbers of the principal nobility and gentry attending him in his expedition, how vain the pretence was that he intended a conquest.

With those Declarations the Prince ordered a letter to be written in his name, inviting the soldiers, seamen, and others, to join him, in order to secure their Religion, Laws and Liberties..."

• From Walter Harris The History of the Life and Reign of William-Henry, Prince of Nassau and Orange, Stadtholder of the United Provinces (1749) p 136-7 : online here.