Just to throw my hat in the ring - I think the North Briton may have run between Glasgow Queen Street and Aberdeen?
Well, you have the right route, but the wrong train! The
St Mungo ran on this route, although in the period that I'm referring to, it was from Buchanan Street rather than Queen Street. I'll give you the point, though, as I'm feeling generous!
I'll also give the rest of the answer to the
North Briton part of the question: it ran between Glasgow Queen Street and Leeds.
As my previous maths (not to say my identification of who's answered!) seems to have gone wildly astray, I think that I'll offer the floor to Mr Aragon, so over to you, sir (and well done!).
Well, having done some reading on Wikipedia, I've learned that St Mungo also went by the name of Kentigern (or Cynderyn in my neck of the woods).* It seems that he has a well in Rippon and Glasgow: might the train have connected the two?
*Why did he become known by the name Mungo? It reminds me of Saint Illtud, who's named-for town Llanilltud Fawr is translated as Llantwit Major. Honestly: Saint Twit?!
Perhaps he was the "holy fool" kind of saint?
Hmmm .... very interesting!