Hi,
You are right, the directories for the time periods show very few McCartin/McCartan in the area, but right across the bridge there seem to be many.Belfast being located with the river also drew a lot of people across the bridge into Belfast to work while living back across the bridge as well as drew people through a residential move from across the bridge. I have noticed that Carton is a name that comes up frequently.
You might find the following of interest on the names, but as this charting is from data contained in 1847-64 for persons with holdings, it does not reflect all persons of the name.
http://www.irishtimes.com/ancestor/surname/index.cfm?fuseaction=Go.&UserID=
It does appear very strange that while an exact address was given for Sarah, only a locality was given for Edward. It appears that a "special" dispensation was made for the marriage. I'm questioning what would need a special dispensation other than being "from another church parish".
He can be placed in Belfast area by 1961 through daughter Sarahs Christening at St. Patricks. which suggests possibly a County Down origination, ( there are many Edward McCartans out of Down) Finding the witnesses John & Sarah Smyth as well might just give the location more exactly. However, there are also many Edward McCartans in the Dublin area.
I had the same problem with many William McIntyres all within the same family tree. To make matters worse they all married Elizabeths. These in turn all had children named William and Elizabeth, Many many large famiilies of fathers, sons, brothers and cousins for about 5 generations made it almost impossible to untangle. I ended up having to trace lineage of all, (and still am working on it), backing the work up by other documentation such as tax lists, military lists, etc... As the time period for the original William wrapped a span that several states were born and boudaries changed frequently, he is actually shown as being a resident in 2 different states at the same time. The original HUGE Virgiia Colony.
Another possibility was that Edward McCartin1st and Mary McAlindon actually were from Scotland. I am seeing many there as well. I think looking into the history for the time periods involved in both Ireland and Scotland for time periods 1780's-1860's would help.
I also noticed that Edward and Sarah did not follow tradtional Irish naming patterns, instead it appears that 1st born son Edward 2nd was named for the immediate father and 1st born daughter Sarah was named for the immediate mother. All children were given Saint names as in keeping with their faith, although naming of the 1st 2 after themselves was not considered very pious and in keeping with strictor Catholic practice for the time. It's actually a direct conflict with Edwards actual given name of Edvardus for strictor practices.It does appear based on web transcripts that this strictor latinization practice was rejected by the Edward/Sarah parental unit, unless auto translation occured when the transcriber transcribed the record. Might do well to send for one or two of the actual record.
If you have more to pass on that might help or have many questions, etc..., you can send through countyantrim@irelandxo.com and it will reach me directly.
Hope this all helps, Jeanette