I don't think H-20 needs to supercruise through its 14000 kM journey. It can fly subsonic for the bulk of the Journey and only supercruise when its making final approach and getting away after launching its missiles. This will save a lot of fuel.
Moreover, with next gen engines with adaptive cycle, it can dynamically change its bypass, thus get into a very efficient mode for most of the journey and then become a supercruising gas guzzling bomber during its final approach.
Also another aspect we need to think about is, does H-20 even need the large weapon bay to hold huge missiles? If H-20 is VLO, then it can get much closer to its target before launching its missiles. It can avoid detection with stealth characteristics. So, the missile it needs launch can be much smaller and shorter range.
Despite progress on Chinese VCE's I don't think they are currently mature enough, but if we are expecting the H-20 to be revealed in 10 years, that may be the case.
What you're describing is basically the ability to perform a supersonic dash when entering hostile airspace. Again designing for this has tradeoffs and benefits. Yes designing the engines to be variable would solve the gas guzzling issue, but unless we are also including a variable geometry wings, designing with supersonic flight in mind, you would need to use a wing with far less aerodynamical efficiency during the subsonic cruise duration. This will greatly affect range as I've commented before.
At best as you can see above, the 245 T bomber with a 25 T payload can reach 11,000km with pure subsonic cruise, a marginal improvement over it's pure supersonic cruise. This is because that aircraft has been designed around efficient supersonic cruise.
Compare that to the traditional B-2 style setup with an extremely efficient wing design. If I'm being real, a similarly sized subsonic cruise with a more optimistic empty weight would be around the same 245T MTOW range but exceed 15,000 km range with the same payload capacity.
