what services would you propose to make best use of the new capacity?
That's the most interesting question for me - I think that a cross-city project that links Queen Street to Central (rather than skirting round the outskirts and failing to serve the city centre proper like "Crossrail") is something that most people would welcome but that can take many forms. A bit like Brexit, you might find people supporting the concept but for very different reasons.
If it ever happens I can only see it as a two coach railway (using the low level stations at Central/ Queen Street and also London's Thameslink/ Crossrail as examples), which limits the number of services.
Should the focus be on the long distance stuff (like through trains from Aberdeen/ Inverness to the south, as happens on the ECML in Edinburgh) or on "metro" services so that there's a relatively high frequency through the tunnel but without creating many long distance links?
I'd go with the latter option, personally, but this then creates the problem that there's a clear imbalance of services - now that the Cumbernauld trains run through to Edinburgh, the only "local" service from Queen Street is the half hourly Anniesland service. It'd be an expensive project if that was the only one to use it!
I'll stick my finger in the air and say that eight services per hour through the tunnel would be an optimal frequency to start with, so what about linking the "Paisley" and "Croy" corridors? Ayr to Edinburgh and Greenock to Anniesland/ Alloa/ Dunblane?
I think that I'd be reluctant to put anything involving single track through the tunnel (so no West Highland or Inverness services) and would want to try to match up "electric" with "electric" at both ends (since it'd make the project even more expensive if you were relying on also paying for wires to, e.g., Aberdeen as part of the project).
But would the flagship Edinburgh - Glasgow service be diluted by extending it through to Ayrshire (and therefore potentially causing more delays)? Might be an interesting political argument to have.