Your biggest gripe can't be solved. P vs PSPACE is a great unsolved problem in computer science (almost as big as P vs NP), and since PSPACE can simulate quantum computer, any solution to your gripe immediately leads to resolution of P vs PSPACE.
That's disproven or just side-stepped given there's already a solution addressing my biggest gripe: factoring. It's been researched and optimized to death on classical computers. Quantum should get a massive speedup. Such a demo of quantum supremacy would be quite convincing even if not 100% proven.
The QC's aren't big enough for that yet. Surely there are other problems ultra-optimized for classical computers, lots of effort at improving them, and might still have a QC algorithm that beats it by QS-supporting speed-up. Something that fits in these smaller machines. Again, the claim that QC did what CC "likely couldn't" would be validated by the effort CC researchers put into doing it without same results.
I doubt their setup had nearly as many person years of R&D thrown at solving it as factoring, sorting, strings, BLAS, certain assembly routines, optimization techniques, etc. There's probably something in those with an effective alternative that's QC-able.
