I've applied your method on more images of the same kind
and I can confirm from my point of view that is a very reliable workflow, it can easily
be automated too. Of course, it can not solve all multiple problems of
a conversion in CMYK, but there are many ways to finish the job.
You also offered me an important food for thought:
"A CMYK fact of life: the lighter the desired color, the worse the possible gamut mismatch. If we were doing pink flowers the problem would be much more severe, and we’d see a lot more variation in the quality of our corrections.”
In my professional life one of the harder (or perhaps The Harder) object to photographers has been Wine Rosè (although I was not involved in the Pre-press), but this is another story...
In the next days, I wish also try to experiment with another strategy: to process again my files from RAW into ProPhoto RGB instead of AdobeRGB and then to follow the same routine. It is interesting because I always thought otherwise, a few times in the past I converted the image in sRGB before CMYK to narrow the gamut before the conversion, obtaining no bad results.
I’ve also tested the suggested channels blending from RGB to CMYK, I think is a very successful technique that I never would have thought about, but
I think it requires more experience, I mean it can be easier to worsen the image.
Last but not least, the tip from Robin Mark D'Rozario, can add a final touch to the image, I think
it will be useful for more than an image in my future workflow.
Once again I wish to thank Dan Margulis for focusing on this case and
to all the contributors who really helped me grow.