If you'll accept some thoughts from someone with far less expertise, I have a few:
* As a general matter, any ICC printing profile is necessarily specific to the printer driver settings, including media type, that were used when the profiling target was printed.
* My usual approach, as a fair to middling amateur / hobbyist, is to look up what media type the paper manufacturer recommends for that paper in the printer at issue, or the most-similar printer for which it makes a recommendation.
*
However, some printer drivers allow you to build your own media types, and even limited to the media types built into the driver, you can test which of them is best. Obviously for a pigment-ink printer with both photo black and matte black inks, a media type that uses the more appropriate type for the paper is important. Other issues include a reasonably-appropriate thickness and ink loading, i.e., volume of ink per area printed.
As I understand it, one of your questions is how to test / determine this. Limited to what's known to me to be currently available, online, with instructions, and free, the only one is at
https://www.on-sight.com/how-to-determine-the-optimal-media-selection-for-any-paper/. I have not tried to use it. It would not surprise me if, e.g., Qimage also has some facility to do this, but I don't know.
* Once you've built or determined the best media type to use, then you print your profiling target etc.
As for, 'Why me and my P7570 / why this Epson now?'--I guess it was Jan Smit and his P9500 instead of you who had the issues with ink apparently pooling on the paper / too much ink. All I can suppose is that Canson has come to a similar conclusion: that the Epson media type(s) otherwise most appropriate for Baryta Prestige and Platine Fibre Rag use too heavy an ink load for those papers, and therefore Canson recommends reducing it by 15%. You could certainly run tests using the test system linked-to above, with say 0, -15%, -25%, and see which works best. And if you find it's -15%, then maybe run additional tests at -10% and -20%. Once you've determined the best setting, you could build or have built custom ICC profiles using that setting.
Or at least, that is what I suppose, based on admittedly-limited knowledge.
