HS2 should run from near Watford, follow the WCML (roughly) then past West of Milton Keynes, pass south of Coventry, through Birmingham airport, go through Stoke then past Manchester Airport to Warrington (ish) where it can rejoin the WCML.
It should be engineered for 300km/h running with the fastest trains getting from "London" to "Manchester" in around 1 hour.
Even after you add on crawls out of Euston, and Piccadilly to Airport then the journey time from end to end is massively reduced.
People can talk about city centres, and getting them served, but ultimately how many people actually live there. Warrington or Airport stations would be as close to people as Piccadilly is, especially when considering the congestion you get accessing the centre of Manchester.
I am not totally sure what the reduction in cost of removing all of the London tunnels and the like would be, but I imagine it would be pretty substantial.
I also appreciate it does little to free space on the line into Euston, but I think it would actually be surprising how many would see a hub station as an acceptable alternative.
If routing is possible the line could then follow the M25 (roughly) to get into HS1 around the massive developments in the Thames Esturary. A journey time of sub two hours from Manchester Piccadilly to Canary Wharf could then be possible.
I doubt Labour have this sort of radical rethink in mind though