Some tentative thoughts on this:
1. the Eastern leg suffers from the geographical location of the key cities en route. Neither Toton nor the original Meadowhall are ideal locations (they make good Parkway stations but are miles from city centres).
2. I can see the logic of splitting the route south of Toton to serve Nottingham and Derby separately. Centre-to-centre journey times should be around 60min.
3. I wonder whether Derby-Sheffield-Leeds would be best served by a substantially upgraded route (inevitably with a fair bit of new build and tunnelling, and probably underground platforms at Sheffield), capable of taking XC services as well as HS2. This might imply a lower maximum speed, but HS1 copes with 140mph Javelins in between Eurostars over similar distances.
4. The question then is what to do about Leeds and the NE. Would Leeds be as well served via Manchester (there would be a time penalty, but then I think I have slowed the Eastern leg too... on the other hand, whichever of Bradford and Huddersfield was the en route stop would benefit, and that gives access to a fair bit of West Yorks!)?
As for the NE - direct from Sheffield to Church Fenton perhaps? Obviously with a stop at Pontefract or Castleford

This might have implications for the Sheffield-Leeds section in 3...
As to service patterns, I haven't got that far, but whatever impacts Covid has will be broadly similar across all routes, so I don't think it's worth second-guessing.
(PS - I am assuming an ECML upgrade to 140mph south of Doncaster is a non-starter).