Out of interest, would a line to Peterhead pass your golden rules? The line via Maud Junction is pretty circuitous, so I was thinking following the Buddon Branch from Ellon with stations at Newmachar (~2,400) Ellon (~10,000) Cruden Bay and Boddam (both ~1,000) and creating a new route into Peterhead (~20,000), hugging the coastline.
Would probably be an extension of the Edinburgh or Glasgow-Aberdeen services, one of them each hour extending to Inverurie, the other to Peterhead. Might be some freight interest in taking fish from the busy harbour too.
It might struggle to compete against the bus which takes 1h10-1h30 and runs every half hour.
It's an interesting one. Traditionally levels of rail usage in the north east have been very low and reopenings have been seen as a central belt phenomenon. However from a low base Stonehaven now generates 500,000 journeys from a population of 10,000 while Inverurie has 400,000 journeys from a population of 12,000.
You'd imagine though that the business case would be much better for a line serving Cults, Peterculter and Banchory which gives you more population, for less capital investment and a shorter journey time.
I'd imagine that Banchory would be the first NE re-opening and if it worked Peterhead might be next on the list.
I haven't seen any mention of these 2 schemes in any official document since the 2006 Scottish Strategic rail study where they popped up in the high resource scenario but didn't have great BCRs.
For what it's worth here are my predicted Scottish rail reopenings in order of likelihood to happen:
1 - Levenmouth. 30,000 people with a 75 minute journey time to Edinburgh.
2 - Grangemouth. 18,000 people with a 60 minute journey time to Glasgow (and a similar
time to Edinburgh with a change at Falkirk Grahamston).
3 - Penicuik. 23,000 people (including Loanhead/Roslin) with a 30 minute journey time to Edinburgh.
4 - Bridge of Weir (either as Paisley Canal extension, or branch from main line) 21,000 people (including Linwood and Houston) with a 40 minute journey time to Glasgow.
5 - Hawick. 18,000 people (including Melrose/Newtown St Boswells) with a 90 minute journey time to Edinburgh.
6 - Banchory. 15,000 people (including Milltimber, Peterculter, Cults) with a 30 minute journey to Aberdeen. The business case is probably actually really good for this one but planners likely to be more nervous when dealing with Aberdeen as there isn't the past evidence of commuting demand that Edinburgh/Glasgow have.