There likely won't be a marriage certificate then, as the Civil registration of births, marriages and deaths started in Ireland in 1864 and in Scotland in 1855
Not quite right. In Ireland non RC marriages were recorded in the statutory registers from 1845. I have searched for a Holmes-McCullough marriage in Ireland 1845 - 1858 but cannot find one. (Nearest was a Mary Holmes – John McCullaugh marriage in Ballymena on 16.3.1865).
Regarding the discrepancies over the women’s names on the marriage and death certificates, mistakes on death certificates are very common. Informants didn’t always have the correct information, especially for items like the deceased’s parents. Given a choice between a marriage certificate and a death certificate the marriage certificate is usually more accurate since the information has come from someone who ought to know their mother’s name.
I also looked for a birth for John McCulloch born c 1872 Ireland with mmn Fox but did not find one.
From her death information, it looks as though Rose Ann Fox was married previously and her maiden name was Anderson. Have you searched for that marriage?
You mention that your ancestors may have been members of the 1st Presbyterian church. Lots of towns in Ireland have more than 1 Presbyterian church so there's dozens of 1st Presbyterians. Any idea which town they may have lived in?