You will need 400m from the stops, plus the length of the new throat pointwork, so at least 200m of the tunnel would have to go but the north end might remain (it's 528yd long). The opened up area would also need to be widened to accommodate however many long platforms there are plus the wider throat and tracks round the edge to reach the remaining short platforms. The disused third tunnel might provide some of this space, but I wouldn't be surprised if the portals are listed.
All of which would have to be done while maintaining some sort of service into the station. The bit of canal above is actually a basin not a simple cut, and judging by what happened at St Pancras would need to be preserved in exactly its present form...
If we sacrifice the suburban platforms as unneccessary in the post thameslink era that substantially reduces the extension to the platforms necessary since they are nearly 300m anyway.
Moorgate could easily handle the residual traffic or they could use one of the long platforms.
While the throat will need to be made wider, it appears it will need to be made wider on the eastern side, which is away from buildings and put it under what appears to be car parking and roads, which prevents massive demolitions.
As to the basin having to be preserved, I think that is primarily an aesthetic matter and there is no reason that you could not have a basin there after construction is complete.
Just that the bridge would have to be wider, although it seems as if the basin is not actually used for anything any more so it might not be politically impossible to simply remove it and replace it with an aqueduct.
With the Thameslink programme Kings Cross has spare capacity as well and would lose most of its intercity services to a HS2 line running to Peterborough anyway.
All that would be left if High Speed went into Liverpool Street would be Cambridge Cruisers really.
Maintaining a service into the station might be difficult but not impossible, it might be easier to simply turn everything back at Finsbury Park and send everything of 6 cars or less into Moorgate permanently to reduce loading there.