Dunbreen and Tattynure were townlands in the Union of Omagh and in the Parish of Cappagh.
Most genealogy services, there are two for Tyrone being Northern Ireland:www.emeraldancestors.com
An Irish History Foundation:
does not have Cappagh specifically but does have close by towns with
RC record but none later than 1900.
Ballygawley 1847-1900 RC
Pomeroy 1837-1900 RC
Termonmagurk/Carrickmore 1834-1837 RC
CofI Sixmilecross b.1836-1871 m:1836-1900
The hamlet of Galbally is 1 m. East.
After reading what you have between the McCutcheon and McFarland's I'm sure you are right that there is a connection.
Parish of Cappagh: email@example.com
Diocese of Derry
You could try writing to both names from Canadian Telephone 411. It will tell you how many and where, full addresses provided.
There are 9 McFarland's in the Cappagh-Dungannon area Tyrone
Ballygawley, Six Mile Cross. No McCutcheon's.
Look for the Irish Civil Registration Record Indexes, LDS 1845-1958 on www.familysearch.org
scroll down the left hand side of page to UK/Ireland, then close to top is
Ireland (6)click on that and see the Index.