To be honest, I'm happy to wait for the BHSE rather than get a Stax amp, simply because the combination of K-01 + Pico Slim + Shure se535's gives me quite amazing SQ. I've never heard the K-03 so I can't comment about it. Before I got the K-01 my previous source was the Esoteric X-03se and the K-01 is in a completely different league. There are other sources that will probably sound as good if not better than Esoteric, but I don't believe Esoteric can be touched when it comes to build quality. Which ever source you decide to get I hope it gives you the SQ you're looking for.
You're probably the only guy on the planet with a K-01 connected to a Yamaha soundbar, lol. I think that would probably make the "bits are bits" guys heads explode.