You'd get punters for dundee easily as although it has a small airport it doesnt get many flights meaning passengers look to edinburgh glasgow or aberdeen. Furthermore its London service is to city, not the easiest if wishing Heathrow for an international connection. Thanks to flybe, birmingham is very wel served domesticly so I'd scrap it. For Brum Heathrow, National Express's coaches are doing this directly and quickly almost 24-7 so wil take a bit of beating. Same for newcastle and leeds bradford, both well served by Scottish air services and fast trains from london which anyone wanting to get home quick enough would use. Also due to ECML paths I wouldnt use it, esp with a bi-mode tilting train. Your market for this is from Scotland and Manchester but particularly Scotland where getting to heathrow can be a big add on to the cost, even if booked at the same time as an onward legg and from some parts of the country, its quite a way to an airport in the first place. I'd suggest:
Dyce, (for aberdeen airport), aberdeen, Dundee, Inverkeithing (for connections with existing Edinburgh airport bus link and local bus and rail services in Fife), Haymarket (platform 0, a bay platform), reverse out to Carstairs. There are wires down to Carstairs but not at your haymarket platform so change traction there and also uplift passengers from a feeder mini coach service from Glasgow, East Kilbride, Hamilton and Motherwell who dont wish to fly to Heathrow or use TPE to Manchester.
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Then on to Carlisle, for existing rail and road connections incl from Scottish borders, Dumfries and galloway and Cumbria, preston, man airport, timing arival to connect with trains from as many places as possible, then nonstop to Heathrow although you could stop at crewe.