Though you can't solve it to be geometrically correct, that doesn't mean you can't find a projection that is perceptually better than all the simple ones. That

Though you can't solve it to be geometrically correct, that doesn't mean you can't find a projection that is perceptually better than all the simple ones. That seems to be what artists are doing with their ad-hoc tweaks. TFA mentions a computerized one near the end that seems to be aiming for that too. Or you could imagine some clever ML algorithm that might treat different objects differently, not just remapping pixels blindly.