Before Civil registration began the Church of Scotland Ministers were, in theory, charged with keeping records of all Births and marriages in their area regardless of affinity to any particular church. 
Unfortunately although some did this many did not, plus there was an onus on the individuals providing the information to the C of S clerks - some didn't as there was sometimes ill feeling between the congregations.
In addition to this the Burgher's went through a number of transitions as the congregations split and joined up with others until some remained with the Free Church and others rejoined the C of S - all records remained with the particular congregations who were their owners.
Another factor is the fire which destroyed the original church known as the "Kiln Kirk" - the "new" building opened in 1846 and was sadly demolished (due to vandalism) in 1976.
They went throught some transitions alright. I went to the NRS in Edinburgh and the Glasgow City Archives and looked the listed collections plus found one more that was quite relevant. ch3/1632 For Pollokshaws United Original Sucesssion 42-47. That had managers minutes, some financial records but unfortunately no baptismal register. 
I started getting confused about the different congregations so made the attached doc to make sense of it. there are a few more contemporary sources that seems to mix up locations and congregations too. Hopefully ive made sense of that . 
They were called Associate Presbytry (Burgher) then in 1799 most of the congregation split and became an Original Burgher congregation (old light) and kept the original church. Where the fennels graveyard is now. The minority of the congregation (new light) went to make a new church on Pollokshaws rd. Its this new chuch that burnt down in 1847 so in my case doesnt affect the records.
The Original Burghers kept the original location and based off dates on birth records held the original birth records (ch3/1636) too (the new light church baptisms ch3/1171 start in 1806 when they got their own church).
In 1841 the Original Burgher minister Finlay Stewart ( the guy who married my ancestor.. and the reason why i started trying to understand these churches and the records kept) died. There was an argument about the new minister. So, some split off to make their own church near Cogan Street (the only one still standing) Pollokshaws United Original Sucession. The records to this as i mention are just minutes etc and not baptism unfortunately. They did in the 1950s become part of COS and then merged with Auldfields Parish church to become Pollokshaws Parish. Theres no SP records for them or any baptisms listed on NRS but i am trying to figure out if the baptism records im after somehow got folded into an as yet unlisted COS record. 
The original congregation got fed up with their organisation so in 1848 joined the free church. they moved to a new location in 1870. The old church became a community hall that eventually also burnt down in 1883. Even though they moved they seemed to retain the original records from the mid 18th century.