there is no rerouting space available
Why not? I can think of several other pieces of Class B or C terminal airspace across the world that are smaller, equally if not more complex, handles more traffic, and fully capable of handling "popup" VFR and IFR transit flights.
Just accept that in the London TMA it is the way it has to be and that will not change for a long long time, if at all.
Not really. This is an unacceptable starter. If you must demand Class A, GA will be demanding Class G and somewhere you will have to strike a balance in the center as is being used worldwide.
Justifying Class A on the basis of airlines and airports PAYING for the establishment of such airspace so that they cannot be "interfered" by other valid airspace users is also an unacceptable starter.
Class C sounds like a good compromise.
I must remind you that your organization is "charged with permitting access to airspace on the part of
all users, whilst making the most efficient overall use of airspace"