Hi Jill
I've been thinking about the discrepancies in dates for David Moffat's birth and death, and wondering how the confusion arose.
When he was buried, the clergyman wrote in the parish burial register-----
MOFFATT, David 64 Mar 20 Jul 1843
------so, assuming that this is a faithful transcription of the original, and assuming that the family gave the correct age to the clergyman, and since his family knew that his birthday was 1st June, then his birth year was 1779. It's possible, though, that they didn't know the actual year of his birth, just a rough idea of his age.
Later on, when the stone was carved, (arranged by his widow, or much later by one of his children perhaps ? ) the exact details had become foggy, so the Old St Runius MI states that he died in 1844 aged 63. If this was correct, he would have been born in 1781, and hence someone supplied those details to the Mormon Church, creating a patron submission of birth date as 1st June 1781. I wouldn't definitely attach credence to this entry, but it might turn out to be correct.
However, the names of the parents from that entry (Peter Moffatt and Helen Mark but probably Mack ) seem credible because David Moffatt and his wife gave Peter and Helen as middle names to two of their children.
I'm guessing that you haven't seen an actual birth entry in the parish register for Dumfries since the birth date you quote is the one from the MI ie 1st June 1787.
In 1841, the census recorded his age as 55 (so could have been rounded down from 59 perhaps, and he could have had his 60th birthday in June 1841)
3 years later at his death, he could have been 63.
If I were searching for his baptism in a register, I'd start at June 1781 and then spread the search to 1779-1783. I'd be surprised if the MI 1787 were correct.
Jean C