Sunfish,
The trick here is to crash through, ala Uber style and build a momentum that can't be stopped - for a kick off, I think the greenies would cheer out loud for such a race. Technological development, electric this, electric that, get the media onside and promote the hell out of it. Get some corporate backing and sponsorship, $10MM first prize, there are philanthropists and corporations around who would stump up that sort of cash given the right marketing and publicity. The idea is to get enough momentum and sufficient reward to encourage development of "green" aircraft, enough push that the regulator gets onboard with the idea and get's out of the way. What a positive thing it could be if someone could make it happen.
All of the problems you list are real, no denying it, but to do nothing is a slow decline into oblivion.
RG,
disagree, there's aircraft available now, off the shelf that could compete. Pipestral Alpha springs to mind. Rolls Royce have developed one. There are other manufacturers developing others as we speak, some I'm sure would love a wide platform and media coverage to demonstrate them on. Conversions to electric can be done. Ultralight electric aircraft. The race could be done under the experimental category.
Pipedream, maybe.
But worth thinking about.