Hi just discovered this site. This is also my family. Mary McIlhearn was my g g grandmother. Also took a while to find them due to name change. I had been told by s cousin they changed their name as it sounded too Irish so they could get work. I see this post was 15 years ago but would be interested to see if any more information on family as thought there were 10 children but can only find 9
There are indeed 10 according to the IGI
Hugh McIlherrin, 28 May 1855
Peter McLaren, 18 October 1856
John McIlheron, 31 May 1858 (the one missing from the lists above)
Catherine McIlheron, 10 October 1860
Mary McIlheron, 23 January 1863
Susan McIlhom, 12 June 1865
James McIlheron, 8 February 1868
William Mackleherring, 17 February 1970
Margaret Mackleherring, 18 December 1871
Rosann Mackleherring, 6 November 1873.
Incidentally I didn't use batch codes. I searched the IGI for no given name, no surname, birth in Lanarkshire, father John, mother Susan McLuskie.
And in answer to the original question, registration was compulsory from the outset, with fines for failure to comply.