Looking for Information about the McLoughlin Family (early 1800's)

I am looking for anyone who may be related to, or know something about, the McLoughlin family from County Mayo in the early 1800’s

My Great (2x) grandmother was Ann McLoughlin who married James Moraghan (later ‘evolved’ into Moore) at St. Chads Cathedral, Birmingham, England on the 28th April 1850. James’ father was Owen Moraghan, farmer from County Roscommon and Ann’s father was John McLoughlin, stroker (?) from Ireland. Ann and James were living in John Street, Birmingham when they got married. At the time of their wedding, Ann would be living with her parents, John and Mary, and James with his uncle/cousin (?), Roger. The various census and church records show that Ann was born in County Mayo.

On the 1841 UK Census Ann (born 1831) is shown as living at home with her parents, John (born 1796) and Mary (born 1801) McLaughin, her brother, Henry (born 1821), her older sister, Bridget Mary (born 1826) and her twin (?) sister Betsy. I know that on the 1841 census ages up to 15 were listed exactly as reported/recorded but ages over 15 were rounded to the nearest 5 years (although this rule was not always adhered to). On the census Ann’s name is given as Mary but was commonly known as Ann (her middle name (?) so as not to confuse her with her older sister, Bridget, who was called by her middle name of Mary). The McLaughin’s were living in John Street, Birmingham. Also living in John Street was Roger Morgan and his family. Roger was from Roscommon and later evidence found his name to be actually Roger Moraghan (a cousin/uncle of James?). 

Ann’s sister, Bridget Mary McLoughlin, married Elijah Cobourne in Birmingham, about 1842, as their first child, Henry, was born Q3 1843. Bridget died in 1892 aged 69 so her birth must have been around 1823.

On the 1851 UK Census John, Henry and Betsy McLoughlin seem to have disappeared off the radar. We know that Ann and James were now married and still living in John Street (Court 6, House 4). Bridget Mary is now married to Elijah Cobourne and a Mary McLoughlin aged 56 is also living as a lodger in John Street (Court 6, House 10) as a hawker and is shown as still being married. Roger Morgan (i.e. Moraghan) is also living in John Street (Court 6, House 5).

On the Griffith’s Valuations there are 59 mentions of John McLoughlin’s for County Mayo and the majority of those are for the year 1856 (Ann’s father was in Birmingham in 1841). In total there are 355 McLoughlin’s mentioned. The Tithe Applotment books give 5 mentions of John McLoughlin in Mayo (between 1825 and 1833) and 15 McLoughlin’s in general.

I had my DNA test carried out by Ancestry and it showed that I am 59% Connacht, Ireland, 37% northern England and the Midlands, 2% Norway and 2% Sweden. I know that my paternal side of the family were from County Roscommon and my maternal side were from County Durham (although my mother’s maiden name is Kelly and her relatives were Ganley’s from County Sligo). I was born in the English Midlands.

I have uploaded my DNA data to GEDmatch Genesis but have (so far) not come across any likely matches from Ireland.

Any help would be much appreciated.