Neville - very many thanks for all the trouble you have gone to - as others have recently in effect said - where would we all be without your help? In this case I would still be virtually wandering around the veldt lost and forlorn.
But I can now bring something to the party. This map is from the Daily Chronicle of 25 April 1900:
Quoting from the text underneath:
"Leeuwkop, called in many of the telegrams Leeuwberg, will be seen in the upper part of the map nearest the left edge. General Pole-Carew advanced from Bloemfontein against Karreefontein and Leeuwkop, sweeping round the position with his mounted troops, so as to attack the left rear of the Boers holding it."
If you obey the instruction in the first sentence you can just make out LEEUWKOP with Karreefontein written immediately above it. Another reference I found did say Karrefontein was just to the south of Leeuwkop in accordance with your map.
From other accounts of 22 April 1900 the 2nd Warwicks took a farmhouse, to silence the Boer pom-poms, at the base of Leeuwkop and then the 1st Welsh came round them and put the Boers on Leeuwkop to flight.
The reason I could not find my man on a casualty list was because initially the 7 wounded 2nd Warwicks were attributed to the Yorkshire Regiment and the name of my man was misspelt. Here is the corrected version from the Army & Navy Gazette of 19 May 1900 but this time not only have they misspelt my man's name but they have got his regimental number wrong - for 3679 A Meaking please read 2679 A Meeking.
I then found this in the Illustrated London News of 3 November 1903:
As for Lizzie Kariefontein she has led me a merry dance. The transcript record I found on Ancestry regarding her death the same quarter she was born is false as she lived to be 86 as this death notice in the Banbury Guardian of 14 May 1987 tells us:
She can also be found in the 1925 Register of Nurses as Carrie Fonteen Meeking and on the 1939 Register as a nurse in a Derbyshire Mental Hospital as Carrie F Meeking but the person with the green pen has written Lizzie Kariefontein above the Carrie F.
I still have two issues - we have three spellings - Kaarefontein/Karreefontein/Kariefontein - which is correct? What was the nature of the wound Lizzie's Dad received on 22 April 1900? Btw besides a place in SA she was also named after her mother who started out life as Elizabeth Ann Brown.