I wonder if anyone can help, I've reached a bit of a brick wall

I tracked down my grandad's birth certificate - ooh what a scandal!
Name: William McCulloch Sloss (
Illegitimate)
Born: 15th February 1892 at Royal Maternity Hospital, Edinburgh
Mother: Jessie Sloss, Domestic Servant - Domicile Dalmellington
Father: Unknown
Birth registered by: mother
Then I looked at the 1901 Census and found:
Address: 5 Linkieburn House, Muirkirk, Ayr
William McCulloch - Head - Married - 58 - Colliery Manager - Worker - Monkland?
John McCulloch - Son - Single - 22 - Mining Engineer - Worker - Ayrshire, Kilmarnock
Jessie Sloss - Servant - Single - 31 - Ayrshire, Dalmellington
Whilst by 1911 I found my Grandad with his adopted parents:
Address: Bellevue Cottage, Bridge Street, Tranent
John Innes (Head) 53, Married, Dairyman, Employer. Birthplace Haddington, Tranent
Mary Innes (Wife) 47. Years Married: 26, Birthplace: Abercrombie, Fifeshire
William Innes (
Adopted Son) 19, Single, Dairyman, Worker, Birthplace: Haddington, Tranent
Georgina White (Neice) 15, General Servant Domestic, Worker, Birthplace: Fife, St Andrews
Jessie Sloss died in 1904 of TB aged just 35.
My mum remembers Sloss's and McCulloch's and indeed Sloss was used in middle names.
Now piecing it together, I reckon that William McCulloch who had a son but no wife meaning she has either left him or more likely in those days died, has been having his jollies with the Servant girl, Jessie Sloss.
To save scandal she's been packed off to Edinburgh to have the baby and have it adopted by what were perhaps family friend's the Innes's - hence naming the baby after her boss. She then returned to her duties in Ayrshire.
Does anyone have any suggestions on what I could investigate next?
There is no birth certificate for a Jessie Sloss around the year she was born anywhere in Scotland. My mum believed that the Sloss line came from Germany - any way to check a list of people who emigrated from Germany?
I believe there are no adoption records before 1930?
I've got my grandad's line from the Innes's but curious about this Sloss / McCulloch connection!
Anything else I could check?