It looked like the "fogginess" was a result of problems in LCMS, most likely related to limited precision arithmetic. I found similar issues in ArgyllCMS, which went away if I used its floating point math options.
Very interesting, and thank you for explaining this again. I had managed not to get it last time. To me, this argues somewhat for making the intermediate calculations in 16-bit linear space. But I'm not sure that strictly follows, or even what's going on.
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