Annie : Barbour tells us that he got his chronology from a table drawn up by Christopher Bowen to fit the work of E. B. Elliott. Both of these men were Anglican Clergy, never Adventists.
You are, of course, correct in what you have said above but Barbour actually derived the 1873 date before reading Elliott's Horae Apocalypticae. He recounts in Evidences for the Coming of the Lord in 1873; or the Midnight Cry, 2nd ed. (Rochester, 1871), pp.32,33:
The midnight cry, or coming of the Lord in 1873, began on the sea...The vessel left Australia with an advent brother on board [i.e. Barbour], who had lost his religion, and been for many years in total darkness. To wile away the monotony of a long sea voyage, the English chaplain proposed a systematic reading of the prophecies, to which the brother readily assented; for, having been a Millerite in former years, he knew right well there were arguments it would puzzle the chaplain to answer, even though the time had passed.
When they came to the 12th of Daniel, the brother saw what he had never seen before, though he had read it a hundred times. "From the time the daily sacrifice shall be taken away, and the abomination that maketh desolate set up, there shall be a thousand two hundred and ninety days." In our explanation of this in 1843, why did we begin the thousand years thirty years before the abomination was set up? Here is our mistake; and it is one of thirty years. The days end in '73, not '43. All this came in a moment. From that hour, says the brother, the whole truth of our position was made clear.
On arriving in London, he went to the library of the British Museum, and among many other extensive works on the prophecies, found Elliott's Horae Apocalypticae, which at that time, 1860, was a standard work; advocating 1866 as the time for the coming of the Lord. There the chronology was found as now given in these pages, with some slight additional proof.
So, I think it would be correct to say, as far as Barbour was concerned, that he initially derived 1873 as the year of Christ's coming from the prophetic periods that Miller had used in his calculations, and this was subsequently confirmed by Elliott's chronology which ended 6,000 years in 1873.
Many others pointed to 1873 but Barbour reached the date simply by reading Daniel together with his background knowledge as a Millerite of the prophetic periods. When nothing happened in 1873, Barbour also independently proposed 1874 as the target year in an article entitled The 1873 Time in the Advent Christian Times of November 11, 1873.
It should also be noted that although Elliott suggested 1914 as a possible date for the end of the Gentile Times, he reckoned the 2,520 years from Nebuchadnezzar's accession year, which he dated to 606 B.C.E. However, Barbour reckoned the 2,520 years from the desolation of Jerusalem in Nebuchadnezzar's 18th regnal year, which he dated to 606 B.C.E. and so calculated 1914 by a different chronology. As far as I know it was only Barbour who had dated Nebuchadnezzar's 18th regnal year as 606 B.C.E. at that time.