My reason for asking where they were in later censuses was so that I could take a look at the originals and see if I could deduce anything. I haven't been able to find most of the census records you referred to.
I did find one, however. I see that in 1851 they were at Goose Eye, Keighley, Yorkshire
George Muir, head, married, 50, paper maker, born Scotland, Edinburgh
Jean Muir, wife, married, 51, house work, born Scotland, Edinburgh
Lillies Muir, daughter, unmarried, 22, paper maker, born Scotland, Edinburgh
Jannet Watson, sister, widowed, 70 or 72, house work, born Scotland, Edinburgh
If their ages were accurate George would have been born between 31 March 1800 and 30 March 1801, and Jean between 31 March 1799 and 30 March 1800. Both of these dates are consistent with their ages as listed in 1841.
It doesn't state specifically whether they were born in the city of Edinburgh or the county of Edinburgh (i.e. Midlothian). So this isn't inconsistent with the 1841 either.
However Lilias' age is inconsistent - she is listed as 18 in 1841 and as 22 in 1851.
You haven't mentioned Janet Muir or Watson, who could possibly provide a clue.
The John Muir in the 1881 census in Edinburgh who was born in Lasswade was aged 62, which if accurate gives a birth between 4 April 1818 and 3 April 1819, not in 1822. What evidence do you have for him being the son of George and Jane?
I see that in 1881 John had a wife Margaret, son William, 24, and daughter Margaret, 20. They look like the family of John Muir and Margaret Young
William, born 23 June 1853, Edinburgh Canongate
Robert, born 12 October 1855, Edinburgh Parish
Margaret Plummer, born 5 June 1860, Edinburgh Canongate.
Because it's 1855, Robert's birth certificate will tell you when and where his parents were born, which may help to pin down whether or not that is your John Muir.
Margaret Muir, other surname Young, died in Edinburgh St Andrew in 1899 aged 73. Her death certificate will tell you whether or not she was a widow, which may help to find her husband's death certificate, which (if he died in Scotland) should tell you the full names of both his parents including his mother's maiden surname.
James Muir and Ann Robertson had a daughter Helen Smart Muir, born in Edinburgh on 25 April 1855. Because it's 1855, that birth certificate will tell you when and where her parents were born, which may help to pin down whether or not that is your James Muir.
There's a listing of a family in Hunslet, Yorkshire in 1861 consisting of
Isaac Muir, head, married, 35, steam engine fitter, born Scotland
Ann Muir, wife, married, 29, born Scotland
Isabella C Muir, daughter, 7, born Hunslet
Helen S Muir, daughter, 5, born Scotland
Ann Muir, daughter, 3, born Hunslet
Alexander R Muir, son, 10 months, born Hunslet
and the GRO web site lists matching children, mother's maiden surname Robertson
Isabella, birth registered in Hunslet, 1853, June quarter
Ann, birth registered in Hunslet, 1857, September quarter
unnamed child, birth registered in Hunslet, 1860, June quarter
James, birth registered in Hunslet, 1864, March quarter
In 1871, at 50 Portland Crescent, Leeds are
James Muir, 45; Ann Muir, 39; Isabella Muir, 17; Helen Muir, 15; Ann Muir, 13; Alexander Muir, 10; James Muir, 7. James sr, Ann sr and Helen born in Scotland; Isabella, Ann jr, Alexander and James jr born in Leeds.
So I reckon Isaac in 1861 is actually James, misrecorded by the enumerator. It would be easy enough to check - just get hold of the birth certificate of one of the Hunslet-born children.
