I've done some thinking and drawn some lines on a map!
Here is my proposed overall scheme, with some annotation:
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HS2 Phase 1 and 2a are left pretty much as they are now. Phase 2b (East) is diverted to south of Derby, where services would join the existing network for the remainder of their journey (although those travelling beyond Sheffield would rejoin the high speed network there. The reason for this decision is the new line I have created, HS East, via Stansted Airport, Cambridge and Peterborough to Nottingham thence Sheffield, where it would join up with Northern Powerhouse Rail (details of which are further down the post). A link from HSE north of Nottingham to where HS2 is curtailed, via Derby, would then complete the Phase 2b network, but serving both Nottingham and Derby. It would also vastly improve east-west connectivity across the Midlands, such as journeys from Birmingham to Cambridge.
I will note, however, that I have done no detailed work whatsoever for these ideas, hence why the lines go through villages, nature reserves etc - they are there simply as an indicative guide. Also, HS2's eastern branch seems to be the only section which follows existing transport corridors (motorways and major roads) closely (or even at all), which negates many of the points anti-HS2 campaigns make about spoiling the countryside; my route makes this a bit more difficult.
Turning to the western side, a new alignment from Crewe to Preston meets the new NPR line from Liverpool to Manchester at a junction east of Warrington (see diagram below). Services from London could go to either Liverpool or Manchester and beyond.
The new NPR (and HS2) line from Liverpool would have a new underground through station in the middle of Manchester (personally I would site it about half way between Piccadilly and Victoria, with underground walkways/travelators to each (ground conditions permitting)) and continue through a new tunnel under the pennines to a location roughly half way between Leeds and Sheffield, whereupon the line would split in two to both cities. In Sheffield it would link up with HSE, and in Leeds a new through station would be built under/next to the existing one, continuing to York.
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That is what, were I to be in charge, I would do (obviously the ideas would be refined and properly developed though!). It gives a new line across the North (scoring political points) and links HS2 nicely with other networks (scoring common-sense points). HSE could be built later when demand is such that more of HS2's paths into London are needed for western services.
I have also included some purely speculative lines to show what the long term future network may look like. The red Scotland branch would only be built if Scotland pain for it though. The Glasgow suburbs bypass should be built regardless of the dotted bit. The line to the north-east would be dependent on demand. Finally a new line from Birmingham to Bristol and the south-west, as recommended in the Greenguage21 report. Again this would be dependent of demand, but I personally think that it would have a stronger case than the Scotland branch (in no way whatsoever am I biased by the fact that I live near this line!).