I don't think there exist any significantly faster private ETH kernels. With your suggestions, I have managed to make the Keccak stages significantly faster, but ultimately the dagger stage clogs the memory controller and defines the hashrate. The algo was designed to scale with memory bandwidth, but in fact it doesn't. The sub-top from both camps perform just about as well as the top range. with the exception of AMD HBM cards, which perform even worse. Pascal will be the same I think.
I've also tried your integrated approach ("free keccak") but I stopped working on it as I figured out pretty soon it wasn't any faster.