Tom,
As usual you provide interesting insights and remind me again why I enjoy history and the fun of research so much.
You wrote, "James II was sitting on the throne in 1688 and couldn't have been playing Bethpage at that time."
There are three sources for the 1688 date that I have seen, and yet they may all be incorrect; on the date, though not the visit.
One of the "official histories" of Thomas Dongan states:
"Thomas Dongan
Second Earl of Limerick, b. 1634, at Castletown Kildrought, now Celbridge, County Kildare, Ireland; d. at London, 1715. He was the youngest son of Sir John Dongan, Baronet, Member of the Irish Parliament; an uncle, Richard Talbot, was afterwards created Earl of Tyrconnel, Lieutenant-Governor of Ireland; and another, Sir Robert, married Grace, daughter of Lord Calvert, Baron of Baltimore. At the death of Charles I, the family, devoted to the Stuarts, removed to France. Thomas served in an Irish regiment, participated in all Turenne's campaigns under the name of D'Unguent and rose to the rank of colonel in 1674. After the Treaty of Nimeguen (1678) he returned to England in obedience to the order of the English Government recalling all British subjects in French service. Through the Duke of York, a fellow-officer under Turenne, he was appointed to high rank in the army designated for service in Flanders, and was granted an annual pension of £500. The same year (1678) he was appointed Lieutenant-Governor of Tangiers. In 1682 the Duke of York, the Lord Proprietor, selected Dongan to govern the Province of New York, then bankrupt and in a state of rebellion. In this office Dongan proved himself an able lawgiver, and left an indelible mark on political and constitutional history. He convened the first representative assembly of New York Province on 14 Oct., 1683, at Fort James within the present boundaries of the city of New York. This assembly, under the wise supervision of Dongan, passed an act entitled "A Charter of Liberties"; decreed that the supreme legislative power under the Duke of York shall reside in a governor, council, and the people convened in general assembly; conferred upon the members of the assembly rights and privileges making them a body coequal to and independent of the British Parliament; established town, county, and general courts of justice; solemnly proclaimed the right of religious liberty; and passed acts enunciating certain constitutional liberties, e.g. no taxation without representation; taxes could be levied only by the people met in general assembly; right of suffrage; no martial law or quartering of the soldiers without the consent of the inhabitants; election by majority of votes; and the English law of real property.
Thus to Dongan's term as governor can be dated the Magna Charta of American constitutional liberties, for his system of government became the programme of continuous political agitation by the colonists of New York Province during the eighteenth century. It developed naturally into the present state government, and many of its principles passed into the framework of the Federal Government. Moreover, a rare tribute to his genius, the government imposed by him on New York Province, 1683, was adopted by England after the American War of Independence as the framework of her colonial policy, and constitutes the present form of government in Canada, Australia, and the Transvaal. Dongan signed the Charter of Liberties 30 Oct., 1683, and on the following day solemnly proclaimed it at the City Hall of New York City. The Duke of York signed and sealed the Charter 4 Oct., 1684; but never returned it, probably for reasons of prudence, for at the time Charles II had, by a quo warranto proceeding, abolished the Charters of New England, and the Charter of Pennsylvania granted in 1684 distinctly admits the right of Parliament to tax the colonies. Dongan established the boundary lines of the province by settling disputes with Connecticut on the East, with the French Governor of Canada on the North, with Pennsylvania on the South, thus marking out the present limits of New York State. By treaty with the Indians made at Albany, New York, 1684, in presence of Lord Howard, Governor of Virginia, Dongan obtained the written submission of the Iroquois to the Great Sachem Charles, on two white deer-skins, and outlined the masterly Indian policy which kept the Five Nations friends of England and a barrier between the English and French possessions in North America, a policy afterwards maintained with success by Sir William Johnson. At the death of Charles II, 1685, James Duke of York was proclaimed king, and New York became a royal province."
The documents that state 1688 refer to the Duke of York being in the colonies and signing this document. This would appear reasonable as the city and what would become the state of New York were named after him and not just the office, and this naming is supposed to have been the action of his good friend Dongan as well.
So it appears that the date will have to be refined to 1684 rather than 1688. That'll teach me to respect some dumb golf writer!