Well if you care to look at Google earth, you've find most of the GCR is intact. There is the odd place south of Leicester where it's built over, but this tends to be limited to a couple of industrial units in one of two places, which could easily be re-located. There is one street of housing at Lutterworth, but space for a new alignment exists between there and the motorway M1.
The problem area is around Nottingham/Leicester, but spurs areas exist for the most part to the MML (so you could access Leicester and Nottingham) and a new alignment could be built around the whole area for relatively modest cost. Sheffield does not require tunnels, if you knew anything about the route, the line still exists through the city.
As for London terminals, there's several options - a new station at Wembley, running into Paddington (which will require less platforms after cross rail) Marylebone or under under London via the met. You need very little extra platform space for a 30 min HST service, or even a 15 min interval one (around 1-2 extra) and there's paths for that on the Chiltern now without any additional platforms. (There's at least 10 spare paths per hour with a similar sort of service you only need the through lines to allow high speed trains to pass - there is just 1 freight train per day. ) The line into Paddington is very underused, service by 1 passenger train per day and a handful of empty stocks. A small amount in single track, would could easily be doubled.
Most of the stations on the GWR/GC Joint had through lines, and there is areas that can be four tracked especially around Denham and North of High Wycombe. Other trains could start form Oxford or Milton Keynes to run north and would be a good way to get freight off the WCML to allow more pendolinos/commuter traffic.
There is still no evidence that any of your costs make too much sense I'm afraid especially as a new HSL has very little difference in construction methods than a new bypass and we'd need 35 miles at most at a rough cost of £1 billion.
The WCML consisted of major remodelling in several locations, basically rebuilding and resignalling 600 miles of railway and £2billion worth of new trains. It's actually not bad value considering the M6 widening is going to cost £60 million per mile, the equivalent of a new lane between Birmingham and Preston or the new runway at Heathrow.