As far as I know, the calculations showing that London will benefit from HS2 and Scotland will lose out are based on the idea that improved infrastructure will lead to more business in the places that are now better connected, and as a consequence one will see a drop in business in those places that are now suffering from connectivity that is worse in relative terms.
In other words, if you want to make areas north of London more competitive compared to the UK capital, you improve infrastructure elsewhere, you don’t simply link them up to London (because this will help the capital, too, which means the relative advantage of placing your business in London won’t be reduced).
From a Scottish point of view, better infrastructure would be wonderful, but it’s really not a high-speed railway to London that will make the difference.
If we look at a map of regional GDP, it’s clear that it’s the Highlands that need help, so direct trains from Inverness to the central belt and perhaps also to Aberdeen would do wonders. In fact, a Scottish high-speed railway (SHS on the map) connecting all of Scotland’s cities would probably transform the Scottish economy. (Proper high-speed trains might not actually be necessary — the physical distance from Glasgow to Inverness isn’t that great, so a relatively straight track and trains driving 100mph would be a huge improvement to the status quo.)
Once SHS was in place, the poorest regions in the north of England could then potentially be connected to it (SHS-E on the map), which would create a lot of growth there, and importantly not just London-driven growth, which would help to stabilise the English economy.
However, Westminster aren’t likely to ever invest in SHS — their tendency to see everything from a London point of view is just too strong, and it’s too expensive to finance through the ordinary block grant. A project like this is something that can realistically only be realised in an independent Scotland.
Denmark recently slapped an extra tax on North Sea oil extraction in order to pay for improvements to the railways. Perhaps something similar could be done here after independence.