I have had a bit of a look for you, but I'm not sure if the Book is going to help you.
(Bearing in mind that I dont have all the book).
I cannot find any reference anywhere to Nor.Ireland and the only reference to the USA was this:
"Many went to Canada and very many must have gone to the United States, but they are difficult to trace. In New York far the commonest spelling is Moody, some of whom may have come originally from Scotland and changing the spelling of their name."
The problem might be that the Book doesn't do a lot to trace Mudies down the line and follow what happened to them. It begins by finding early Mudies from as early as the 1500's and listing their descendants down to the late 1700's. But it is very incomplete, and in some cases gives names of children but no dates.
The Book mainly concentrates on 2 families, named the First Family & Second Family, who appear in the Burgess records of Dundee.
I would say you have no links to either of these families. Both have some of their descendants listed with births in the mid 1700's, but there is not one James in the family over three generations, which is unusual as James is apparently one of the most common Mudie names and you would think that if your James fitted into this family there would be other James ancestors whom he would be named after.
There is a chance your James fits into the family known as the 'Mudies of Pitmuies'. There are James' in this family but no dates given and certainly no info about what happened to the descendants
QUOTE FROM BOOK
"MUDIE OF PITMUIES
The Pitmuies family originated in Arbroath. James Mudie who bought the estate in 1769 is described at his marriage in Dundee as "in Aberbrotick" and his brother, David, was the David Mudie mentioned above who was a member of the Arbroath Town Council. James and David Mudie are said in the "Family Tree" to be the sons of James Mudie and Helen Fairweather of Bryanton, the daughter, possibly, of Thomas Fairweather, who acquired Bryanton some time after 1711. This may be accepted, particularly as the name Helen occurs in the next three generations of the family. Where the "Family Tree" seems to be wrong is in stating that James Mudie, the husband of Helen Fairweather, was the third son of David Mudie, Second of Gilchorn. This David Mudie was married in 1664, so his third son, James, was, almost certainly, born not later than 1675 and would, therefore, have been eighty-six when his eldest son, James, was married in 1761, and ninety when his younger son David was married in 1765. This is not impossible, but it is so unlikely that it must be ruled out. If James Mudie, who married Helen Fairweather, was a descendant of David Mudie Second of Gilchorn, then he must have been a grandson and not a son. The Moodie Book suggests that he was the son of John Mudie, a son of John Mudie Third of Gilchorn, who was baptised at Lunan on 1st March 1701. This may be so, but it is only a conjecture.
Some light is thrown on the origin of the family by the statement in McBain's "Eminent Arbroathians" that about 1740 John Wallace's agent for buying flax in Riga was his brother-in-law, John Mudie, "one of the Mudies of Pitmuies", by which, presumably, he meant a near relation of the James Mudie, who __ later acquired Pitmuies. This is particularly interesting as James Mudie acquired Pitmuies from Archibald Douglas of Douglas through James Pierson, merchant in Riga. Pitmuies is a much more important pro- _ petty than either Arbikie or Gilchorn, and must have cost a good deal of money. The inference would appear to be that this money came from trade with Riga in flax. John Wallace's wife was Elizabeth Mudie, whom he married in 1729, and John Mudie, the merchant in Riga would be her brother. James Mudie, the husband of Helen Fairweather was, probably, another brother and may have been the James Mudie, merchant, who, as we have seen, was associated with John Wallace in lending money to the Town Council. The Mudies in Arbroath were clearly related to those of Gilchorn but it would seem more likely that the father of James, John and Elizabeth Mudie belonged to a merchant, or possibly a lawyer, family in Arbroath than that he was a son of the laud of Gilchorn. But, of course, there is nothing unlikely in a laud's son becoming a merchant in Riga.
The Pitmuies family would thus seem to start with one James Mudie, merchant, who had a brother John, who was a merchant in Riga, and a sister, Elizabeth, who married John Wallace, "junior". James Mudie married Helen Fairweather of Bryanton, and had issue:
(1) James Mudie
(2) David Mudie, d. April 1788(3): married Mary Geikie, whose mother was a Wallace, on 27/4/1765 at Arbroath, and had issue:
(a) Helen Mudie, bapt. 29/7/1766: witnesses Provost John Wallace and Mr. James Mudie.
• (b) James Mudie, bapt. 31/1/1768: witnesses Provost John Wallace and Bailie George Kyd
(c) Katharine Mudie, bapt. 27/8/1770: witnesses Provost John Wallace and James Mudie of
Pitmuies, Esq.: married John Colville, Town Clerk of Arbroath.
(d) David Mudie, bapt. 28/5/1772: witnesses Mr. George Kyd and Mr. Alexander Mudie. (e) Elizabeth Mudie: married Alexander Hutchison of Arbroath.
(3) Helen Mudie(4): unmarried.
The names of the witnesses are interesting as confirming the Wallace connection and indicating that Alexander Mudie, the Town Clerk, was a relation.. So is the change from "Mr." to "Esq". in the designation of James Mudie after he had bought Pitmuies.
An account of David Mudie's membership of the Town Council has already been given up to 1665, when he failed to be elected a Bailie. A vacancy must have occurred later in the year because on 29th June 1766, at the baptism of his daughter, Helen, he is described as Bailie. He is similarly described on 31st January 1768, at the baptism of his son, James. On 27th August 1770 and 28th May 1772, at the baptisms of his daughter, Katherine, and of his son, David, he is described as Provost."
The spelling of your Moody's should give you hints where they came from. The Book claims that Mudie names do not change or vary in the records. 'Mudie' usually indicates Angus origin, 'Moodie' indicates origin from other parts of Scotland (Glasgow, Edinburgh & Fife) whereas 'Moody' is an English spelling of the name.
I may also be able to help you if you tell me what James' occupation was. The Book looks at occupations and who the originators were. Do you know James' occupation?
I hope to have a full copy of the Book soon, and if I do, I'll have another look for your James.