The most obvious observation here is that it’s possible that the Leitrim townland in Co. Antrim has been confused with the County of Leitrim. The two are 100 miles apart and it would be surprising for two brothers to be born so far apart. Most Irish people stayed in the same broad area all their lives. Obviously a few moved if their profession demanded that eg a policemen or such but most didn’t. You would expect them to both come from more or less the same place.
Leitrim is a common townland name in Ireland. There are 40 including 2 in Co. Antrim. One in Drummaul parish and the other in Ballymoney.
Leitrim in Drummaul is on the modern Staffordstown Rd, not far from Creggan Primary school. A mile or two from Randalstown. It’s 165 acres in size and in the 1901 census there were 12 homes there and a population of 55. No Heaneys.
http://www.census.nationalarchives.ie/pages/1901/Antrim/Randalstown/Lei…
I checked Griffiths Valuation (1862) and the tithe applotment records for 1833 but there were no Heaneys listed there then either.
Drummaul RC’s parish records only start in 1825 so if that’s where the brothers were baptised in the early 1800s there are no records to search.
I have a copy of “Sweet Drummaul” by Patrick O’Kane which is a history of the Roman Catholic parish. It mentions a Hugh Heaney as living in Magheralane in 1848, in a list of all the parishioners. That appears to be the only Heaney family in the parish at the time, though obviously there might have been others earlier who had left. (People were pouring out of Ireland all through the 1800s). Magheralane is a couple of miles from Leitrim. Sweet Drummaul also contains the emigrants list which you have provided, and which was in turn taken from the Ordnance Survey memoirs of the parish. It lists Catholics who left the parish between 1835 & 1837. Hugh Heaney of Leitrim was 26 so that fits with him being born around 1810 or thereabouts. He is noted as having gone to Glasgow. That was very common. Huge numbers of Irish folk went to Scotland from Ulster then as there were much better work opportunities in Scotland. Many then left Scotland after a few years, having raised the fare to emigrate, and went to to other countries. It’s called stepped migration.
It looks to me as though the Leitrim Heaneys were labourers who had a small cottage (rather than a farm) and had all left that townland by 1862 if not a lot earlier.
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project in conjunction with FTDNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).