You haven’t said what denomination the family was. I assume Church of Ireland since that’s the only denomination with any records for Caledon in the 1700s and I see John Mossman in the 1766 census of Aghaloo & Carnteel is listed as protestant. I assume you have searched the Church of Ireland records for John’s marriage and burial. Those baptism, marriage & burial records all start in 1792 but there’s a gap between 1796 and 1800, so any events before 1792 or in the missing years are lost.
Tradition was to marry in the bride’s church, after which she’d usually attend her husband’s. So it’s possible that John’s marriage was not in Caledon Church of Ireland. If so, you would need to know where the bride came from and what denomination she was. You would also have to hope that the church in question has records for that period (many don’t). In the late 1700s people married close to home, because most courting was done on foot, but she might have come from an adjacent parish or she might have been of a different denomination eg Presbyterian.
Here’s a map of all the parishes in Tyrone:
https://www.ancestryireland.com/civil-parish-maps-for-ulster/civil-parishes-of-county-tyrone/
This link explains what records exist, parish by parish. In most cases there’s a copy in PRONI
https://www.nidirect.gov.uk/publications/proni-guide-church-records
Statutory death registration only started in 1864. Before that you are heavily reliant on gravestones and burial records. Not everyone could afford a gravestone, and even where a family does have one, not every burial is noted on it. Only the Church of Ireland kept burial records, and even then the record keeping was patchy. I assume you have tried the various pay to view gravestone sites covering that area.
If John was buried in Benburb or The Moy all their early records were burned in the 1922 fire in Dublin. They have nothing now before 1881, so if that’s where he was buried there won’t be a record, unless he is named on a gravestone or is mentioned in a newspaper.
I had a look for the family in an on-line newspaper site. A few mentions of Mossman from Mullycarnon where they evidently had an 82 acre farm. John Mossman was trying to let it in 1840, Carlisle Mossman was a juror at Tyrone Assizes in 1849 and John & George were mentioned in 1839, again offering leases on land. The Dublin Evening Post for 12th August 1848 has an item relating to Dr John Sloan, formerly of Caledon, who had died in Franklin County, Pennsylvania. He left an estate of $3000, half of which was to go to a friend, also named John Sloan, who lived near Caledon, “who was born between the years 1790 and 1796, near that town, and whose mother resided for some time previous to his birth in the family of John Mossman, a few miles from Caledon.” The purpose of the notice in the paper was to advise anyone who believed they had a claim on this estate to contact the court in Chambersburg before the third Monday in January 1849. I did not find any burial notices for the Mossman family in the newspapers.
