I think you are being a little overoptimistic. Borders Rail is costing £300m for 30 miles, construction started in 2012, and it's not electrified.
You are uninformed and not comparing like with like. Borders Rail is 31 route miles and 41 single track miles fully signalled with 10 platform faces and 7 sets of 60mph points and cost £280m.
Harrogate-Ripon was costed in 2006 at £36m for 9 single track miles, one platform, signalling at former Dragon Junction only using one 60mph turnout operated as one engine in steam. If planned and installed simultaneously with Harrogate-York resignalling in 2020, the junction cost could be as low as £8m.
No bridges need raising for electrification clearance and if installed during reinstatement should cost no more £500k per mile. Overheads would be fed from Harrogate loop electrification with one section cabin at Dragon Junction.
Yes at 2015 costs we are probably looking at £60m but construction of only 9 miles would only take 15 months. Tracklaying would be less than a fortnight.