I'll mention the following three things for you to consider.
Firstly, the "scotlandspeople" baptism index shows a Catherine Murray baptised (RC) on 12 April 1838, parents recorded as John Murray and Matilda McHaffie, the parish was Glasgow, St. Andrew's. I couldn't readily see a marriage for them.
Secondly, there was a marriage in St. Peter's RC Church in Belfast on 30 March 1900 between a widowed bootmaker called Thomas Murray, son of a shoemaker named John Murray, to an Ellen Savage:
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1900/10342/5765230.pdf
On it's own, of no great import... except that the RootsIreland subscription website has a transcript of the church record of that same marriage which also identifies Thomas' mother - namely one "Matilda Mahaffey". When I go looking for Thomas a year later in the 1901 Ireland Census, the following looks like a possibility, with Thomas' birth indicated c. 1846 in Scotland:
https://www.census.nationalarchives.ie/pages/1901/Antrim/Falls/Cyprus_Street/951042/
The Thomas in that census return died on 7 December 1908 with a reported age (by his wife) indicating birth c. 1851:
https://www.irishgenealogy.ie/files/civil/deaths_returns/deaths_1908/05481/4534962.pdf
Thirdly, the following item in the Newry RC registers is difficult to read, but if you fiddle with the light and contrast, you should be able to make out the baptism of a Jane Murray on 28 February 1848 for parents John Murray and Matilda Mehaffy, sponsors Thomas [something] and Mary Gallagher:
https://registers.nli.ie/registers/vtls000633289#page/31/mode/1up (left page)
Forgive me if I am misunderstanding, I'm so excited to have had replies that I may be rushing through reading.
I had suspected, based on the existence of records indicating another McHaughey/Treanor/Murray convergence in the same area as my ancestors in Glasgow that perhaps they had had pre-existing connections there before they moved there themselves.
I thought maybe they were unconnected and I had stumbled upon them simply by virtue of looking specifically for those names, but the physical proximity did give me pause. Would these records indicate to you that perhaps John and Matilda McHaughy/Mahaffy/whichever spelling were themselves from Scotland? I had thought maybe that during the famine years they had maybe been travelling between Ireland and Glasgow for work, given that there can't have been much to go around for a shoemaker, but I am very very much an amateur and have nothing but my own speculation to back this up.
Thank you so so very much for replying!
