Hi I didnt find what you seek and you already have a lot, but just in case one item or more is new to you here goes
You probably know
www.bagenalscastle.com/ancestryI found I didn’t know where is Ballynahatten, but its Kilkeel! My reason was I found a match for Reid and hanna in the same townland in the agriculture 1803
George Hanna Ballynahatten
John Reid Ballynahatten
However elsewhere I found a possible follow up
Crossle Papers
Hanna 326 Genealogical notes
Ros Davies
http://freepages.genealogy.rootsweb.ancestry.com/~rosdavies/A quick incomplete search revealed
William REID . Newry of Desert ; father of Mary bpt. 1 Jun 1815 & Samuel bpt. 31 May 1824 at Old Newry Non Subscribing Presbyterian Church PR
Miss HANNA Newry lived in Desert townland in 1851 census; married Reid OFN p 228 This is an unusual ref its from OFN Old Families of Newry by R.S.J. Clarke Ulster Historical Foundation 1993, because the 1851 census is now on line at national Archives and I could find no references to Hanna or Reid
Alexander HANNA . Newry of Desert ; father of John bpt. 16 Apr 1826 at Old Newry Non Subscribing Presbyterian Church PR
I think the church mentioned is
Old Presbyterian: Unitarian then Covenanters (Non Subscribing)in High St, Newry
The congregation originally met in Sheepbridge in 1763 then they built a meeting house behind High Street, Newry in 1782. This site was later abandoned in favor of the church in Downshire Road. The street was renamed John Mitchel Place.
Graveyard attached called Little Green, gravestone inscriptions available UHF Vol 21 ; email me Ros Daviesfor a gravestone look-up. However Ros doesn’t mention the records location, so
try PRONI online quides –Church records. Presbyterians were some times buried in C of I graveyards
So that is all I can do on your query, lets hope others can help properly
JimG