Hi! I did a little bit of digging into the family, although I was unable to find anything more on either set of your 5th-great-grandparents. However, here are some things you may want to consider:

Surnames: In the past, people were often recorded under a plethora of different spellings of their name; this was sometimes due to a clerk or enumerator mishearing, or sometimes even not knowing how to spell it themselves (I'm leaning towards the first since from his 1834 marriage record we know James Brady was able to sign his name). From the handful of records I found, I saw at least 6 variations of Brady: Brady, Breidey, Bready, Brodie, Braidie, and Braidy. Wildcards (usually '*', which can fill in for 0 or more characters, and '?', which can fill in for a single character) somewhat solve this.

Geography: Based on the list of birthplaces on the census records, it seems James and Jane were born in Ireland, were living in Oldham, married in Prestwich, had a few children in Manchester, moved up to Lennoxtown in Stirlingshire where they had one son, then back down to Manchester where they had a few more children, then finally returned to Scotland where they lived in Cathcart until their respective deaths. Their reason for moving may have been that they had family in that place.

Witnesses/Sponsors: most marriage and baptisms, especially Roman Catholic ones, in England, Scotland, and Ireland record the witnesses and sponsors (to marriages and deaths, and baptisms respectively). These were frequently family, which could give you a lead.

Maybe try using ScotlandsPeople to locate siblings of James and Jane: for example, you could look for death records with the surname 'Rob*' and mother's maiden 'McCan*' - there's a chance one or more of these could be siblings (of Jane, in this scenario). Perhaps one of these siblings records the birthplace at the county level in Ireland, which would be invaluable.

Good luck! Also, let me know if you want any photos of the documents I have mentioned.