Its already been stated that the Western alignment is prefered as it primarily benefits Glasgow a much larger city than Edinburgh, because of the Geography of the country going east it would be a longer route as it needs to go west again (Edinburgh is north of Manchester and Glasgow is West of Manchester, both are well west of Newcastle)/
Remember that you are eating up track at the rate of 5.3km every single minute. The distance travelled within reason is effectively irrelevent.
An important factor is the
total amount of track required and since a E-G HSR line is going to be constructed anyway you effectively only need 105 miles to get between Glasgow and Newcastle, and then you have an already priced line to York where you join up with the end of the Leeds branch of the HS2-2 plan.
Attempting an up the west coast route requires 210 miles of track between Wigan (the northern end of the Manchester branch of HS2-2) and Glasgow, and then a spur to Edinburgh since it is unlikely that these journey time fetishists would be satisifed with looping around using the existing E-G link.
So overall you end up requiring similar or even more track for less actual population served, all for a few minutes to Glasgow on a several hour journey.
Precent exists for such a routing via population centres instead of a point-to-point connection in the LGV Nord which is routed via Lille rather than in a straight line between its two primary end points (Paris and the Channel Tunnel).
and because theres still a lot of unused capacity on the ECML between England and Scotland. So far the only ones who have even suggested an eastern alignment was Salmond when he was lobbying Councillors in Newcastle to support HS2 phase one and two and not oppose it because it didnt reach them.
But aren't we constantly told that there is no room in the timetable for an Edinburgh-Newcastle stopper, requiring EC trains to stop at numerous irrelevent destinations that would never, in the normal cause of things, justify a significant InterCity service?
The Scottish Partnership Group (Network Rail, CBI Scotland and Transport Scotland) in January proposed that HS2 was extended from Leeds to Newcastle and from Manchester to Scotland and that people in Newcastle to Scotland could use the existing connections.
Yes, but this assumes that the choice is between a western alignment and an eastern alignment.
But the choice in an independent scotland could quite easily be between an eastern alignment and
no alignment.
And remember that it is probably rather naive to believe that an alignment to a Newcastle that is not on the route to Scotland would ever be built.
The Government would baulk at the >£4.5bn price tag.
They would just hide behind the classic compatibles and say that no new spur would be required.
It would certainly be behind Liverpool in the queue since rather less track is required for a similar population/time saving to Newcastle.
(Especially if its a short northern link from Wigan to the vicinity of the former Exchange site).
EDIT:
And As to a second High Speed Line terminus, I like Paddington myself, it points towards other parts of the country that could get a service in future (Great Western area) but could still potentially serve as the end of a second route to the vicinity of Birmingham.
Hell remember that we don't even have to have stations be on the same side of London as the route they serve (see St Pancras), so we can use whatever terminus is convenient, and Paddington has a nice easy access route that means we only has to demolish a single office building to get the long platforms in and will have spare platform space as it is thanks to Crossrail.
Much easier than say... Liverpool Street.
Although Kings Cross is also doable if you put the canal north of it onto an aqueduct over the very end of the platforms.
and when you think you are being factual gives us a 
Most of us will then go :roll::roll::roll: and say you are :-x