Dear all, thank you for your responses. I have looked further into the problem and this is what I can report.
The good news: I can get accurate results if I use the output profile to render the main histogram and Navigator, provided that I tag the input file (that is embed a profile), choose to use the embedded profile, and set the same profile as an output profile. I can also set a different output profile: then the input file is converted to this profile (Lab values are preserved, RGB values adjusted). If the input file is untagged, then I am OK if I use as custom pofile the profile of the space in which it was created and also set this (and only this) as the output profile. Changing the working profile has no effect. This behaviour is more or less as expected. The bad news: no other settings seem to work. In particular, if I choose the option to use the working profile to render the main histogram and Navigator, then results are completely unpredictable.
What I would expect: if I choose to use the working profile to render the main histogram and Navigator, then I would expect this request to be honoured (if my input file is correctly tagged gamma2.2, and the working profile is gamma2.2, then dispayed RGB and Lab values should be correct). If the input file has an embedded prifile then this should be respected (either converted to the working profile or with the working profile applied, in photoshop terminology).
It would be useful if somebody could clarify this for me. Is this behaviour as expected? Could somebody explain how profiles are actually managed, and the rationale? Obviously I have found by trial and error some settings that work. But I would be more confident if I understood how the system worked as a whole. As requested, I have uploaded relevant files to Filebin 3r3wrbeyukj6z3b4