The IGI has three Cumberland Andrew/Jane marriages within 20 years of 1774 (Stephen's birth), two are in the 1780s and therefore too late (Jane Graham Kirklinton, and 1785 Jane Collin at Plumbland, so my current favourite is the 1765 one at Kirkandrews upon Esk to yet another Jane Graham.
The Kirkandrews-on-Esk marriage entry reads: Andrew Graham of the Parish of Arthuret and County of Cumberland, a batchelor and Jane Graham of this Parish of Kirkandrews upon Esk, Spinster were married in this church by licence 17 July 1765. Witnesses William Graham & Elizabeth Wilson her mark", which places this Andrew in the right parish.
And then the Carlisle Marriage Bonds clinched the id for me: Andrew Graham of Fald, Parish of Arthuret, Husbandman Jane Graham of Lake, Parish of Kirkandrews upon Eske, Bondsman William Graham of Carlisle, Shoemaker (the Record Office adding that the Dormont Book Carlisle shows William Graham was the son of Ellin Graham of Lake, and almost certainly Jane's brother)
Sources
WikiTree profile Graham-2165 created through the import of HENDERSONLornaAncestorsPlus1Desc4WikiTree.ged on Oct 18, 2011 by L Henderson.
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DNA Connections
It may be possible to confirm family relationships with Jane by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Jane: