I don’t know if you have solved your Livingstone problem yet, but if not I may be able to help.
Your great great grandmother, Elizabeth, was married to Thomas Forrester Thompson and had ten children. One of these was Tom who married Katherine Brooke Shires and had five children under the surname of Brooke-Thompson. The youngest son, Brian, married Petrina Fry, my eighth cousin, 1x removed, so we obviously have a family connection. Although born and bred in England, I have been living in the Canary Islands since 1967, but retain a home in UK, which I was visiting several times annually up to a few years ago, to do genealogical research. I saw your messages on internet last week and decided to do a little research. I have traced as many as possible of the descendants of Robert & Janet Christie down to the mid twentieth century and think that some of those still living may have an answer to your query Three of these are ladies who were born in the 1960s and are direct descendants of Jessie Christie, daughter of Robert & Janet and sister of Elizabeth. Their family is known to hold a lot of family history information, but I am unaware if they have anything on the Livingstone connection. They, like you, live in Australia and it should be relatively easy for you to contact them.
I would be very interested in making contact with you, to tie up a few loose ends I have on the Thompson side of the family.
Kind regards
Keith