Would it be easier to upgrade the ecml for 140mph+ running north of York? The ecml has always been traditionally straighter, mind you though you would have to do a lot of quad tracking and potentially tunneling to gain enough paths and iron out some kinks. On second thoughts abandon it :-P
I doubt it would be significantly cheaper, especially with all the tunnels needed in and around Durham.
And this way you get gauge clearing for free.
If you approach Newcastle from the south you can probably gauge clear the King Edward V Bridge for a single track of high speed rail, although only having three tracks in the approach might force a reworking of the local services so that they all head south over the High Level Bridge to free an approach line.
Can slew the northernmost platforms over and extend them into the car park where the old suburban platforms used to be to give a through 400m pair of platforms.
58m or so to Edinburgh from Newcastle, and you can potentially manage approximately 1hr40 to Newcastle with a stop at OOC only.
That gives you ~3hr05 to Edinburgh even with no upgrades to the classic line between Edinburgh and Newcastle.
Journey time to Glasgow depends on the exact arrangements for the Central Belt HSR.
But even so, I am sure there are lots of low hanging fruit on the EDB-NCL line in speed terms.
SNCF modified a standard TGV into a tilting prototype due to political pressure in the 1990s, and I believe this reached 320km/h on non-tilt sections and 220km/h on tilt sections.
And was taken no further despite said pressure, which says something about the viability of the project I'm afraid.
Otherwise I would be agitating for all new Inter-city stock to be similarly specced to allow the installation of such equipment.