See
http://en.wikipedia.org/wiki/Thames-Clyde_Express
When Northern (or was it Arrive back then?) ran Leeds - Glasgow, the services were fairly well loaded whenever I used the service. As you've said, running through to Hull or somewhere would probably increase usage. A service like this would be well suited to a 22x as they'd have have speeds for the WCML good acceleration for the S&C. Good pathing combined with limited stops on the S&C could produce fairly fast timings too.
I know of the old train, but that's of no use now that the Virgin and National Express routes are so well established and are much faster. No point duplicating Sheffield to London either, which has a good service (well... let's not go there...)
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Don't think you'd get a crew from London-Carlisle.
Queen Street to the South is possible, but not a great route. You'd be crossing over the city quite a lot and it's really not a feasible passenger route. Also, Queen Street's getting quite congested from what I understand.
Motherwell-Stirling via Coatbridge will take a while because the line speed is quite slow, but it's not impossible in an hour.
And remember that the Far North Line isn't a great line! As has been said, there's a reason it doesn't have half hourly trains along the full route; it's length and the fact it runs through the middle of nowhere! The reason there aren't many paths is because there's no point investing in more passing loops.
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The big part missing from the network, IMO, is a NW-SE XC service.