Hello Kim, I have a copy the Rutherglen Old Church Monumental Inscriptions published by the Glasgow and West of Scotland Family History society.
There are two mentions of Scott.
One is that they had Lair 721 - 725 but there are no inscriptions.
The other is for lairs 993 - 997.
I shall transcribe the inscription in case any of the names are known to you.
" Erected by ALLAN SCOTT jr. in memory of MARTHA STEPHENSON, his wife, who died 9th Oct 1865, aged 26 years. AGNES FREEBAIRN, his mother , died 30th July 1865 aged 58 years. AGNES M. SCOTT , his sister, died 18th August 1837 aged 15 months. ARCHIBALD SCOTT, his brother, died 6th Match 1853 aged 12 years. JANE SCOTT, his sister died 25th April 1858 , aged 15 years. ALLAN SCOTT, his grandfather, died 13th January 1863 aged 77 years . JANE LANG, his grandmother died 25th January 1863 aged 79 years. ALLAN SCOTT his son died in infancy 18th september 1868. JAMES A. STEVENSON, died 6th February 1874 aged 19 years. The above ALLAN SCOTT died 20th April 1878 , aged 45 years. His daughter MARTHA STEPHENSON SCOTT died 19th September 1943 aged 77 years. "
I'm afraid that's all Kim. No sign of any Gib name.
Good luck ,
Baird