Hi Jean,
There was a Loyalist Ebenezer Ward, but I'm not sure about the Massachusetts place of birth, or the other information. The Loyalist Ebenezer Ward was in Digby Nova Scotia: The New York Genealogical and Biographical Record, Vol 34, page 196 lists Ebenezer Ward in a muster roll of disbanded Loyalist officers in Digby dated May 1784, with a wife, a child under 10 and a servant over the age of 10. It doesn't give his rank, but perhaps the New Jersey records will shed some light on that. He is referred to in the History of Annapolis and the history of Digby.
I can find no records in Essex Mass for a man of the right name and age on FamilySearch or American Ancestors.
I do see conflated trees online that suggest he was born in 1737 in Salem (this Ebenezer Ward married Mehitable Buttolph and died in 1770's), and born in 1777 in Attleboro, who married Mary Barnes (too young), or the Ebenezer Ward in Plymouth who married Lydia Polden in 1765 (seems to have been a Revolutionary soldier).
I also see an interesting reference in Jamaica, Queens County, New York, where a number of Loyalists lived during the Revolution. This is in Volume 14, page 242 of the Mayflower Descendant. It lists, among the children of Thomas and Joanna Ward, Ebenezer born January 13, 1747 in Jamaica NY. Could there be confusion about the reference to Jamaica?
The only other breadcrumbs I can find are a handful of land grants in 1810 and 1816 in New Brunswick, but these went to another Ebenezer Ward completely: he was born April 10, 1775 at Sackville, NB, the son of Nehemiah Ward a New England Planter who left Attleboro Mass for Sackville circa 1762, where he married Susannah Salisbury. Their son Ebenezer married Mary Barnes November 9, 1797 and had at least 11 children in Sackville. The land grants mention his brothers: Phineas, Elisha, Daniel and Thomas.
I hope this helps.