Thank you. That is extremely helpful. I will pass this on.
Regarding newspaper death announcements, I can't find anything but I am not quite sure where to look. There doesn't appear to be anything on Find My Past and The British Newspaper Archives for Hamilton, Lanarkshire only cover up to 1949 as the Bent Cemetery burial records do. Unfortunately, we are looking at 1952. For my own research, which is also relevant to my cousin for another branch, I got a lot from The Greenock Telegraph but I am not used to searching for Hamilton.
I think an enquiry to the Bereavement Services is a very good idea.