Following up on my last post, I went back into that photograph, turned off the Curves adjustment layer, and indeed that wiped out the clipping you mention. In fact, I should not have clipped it at all in the first place - it was a bit of poor curving on my part. I can achieve the desired contrast under soft proof without clipping. That improvement, however, has no impact on the basic problem.
So now the interesting part: I once again decided to have another "GO" at those reds in Photoshop, with something pedestrian - a "Selective Color" adjustment layer. Leaving soft proof activated, I went into RED, decreased Magenta by 37%, increased yellow by 28% and increased Black by 9%. These three tweaks didn't produce a soft-proofed red that truly resembles the hue of Chinatown red, but it dramatically reduced the purple to an extent that the overall effect is somewhat more realistic. I'd still like to be able to do better.