There is indeed difference in thickness between the various 310gr/m2 papers, Rag Photographique is for example Edition which has been flattened.
Arches Aquarelle Rag 240 g/m2 = 18,42Mil, 468u
Arches Aquarelle Rag 310 g/m2 = 23,38mil, 594u
Edition Etching 310 g/m2= 18,65Mil, 479u
Rag Photographique 310 g/m2 = 18,34Mil, 466u
Montval Aquarelle 310 g/m2 1 = 19,52Mil, 496u
I see no good reason why your printer should not print on any of the Canson Infinity papers, I have found that the very best range of all, superb black, and very nice caracter in the details, looks like their coating on top of the traditional high-class art papers works much better than any of the ordinary photo papers I have investigated.
My recomandation is to try Edition first for all you needs, BFK Rives is best for Gicklèe, and off course Montval for Aquarels. Photosatin 270 is nice for posters, and for some black/white printing many prefer Baryta, but I think it looks better on Edition.
I make my own media settings for each paper for the printer, and off course I make ICC profiles for each combination printer/paper. If you have one of those new 12 colour printers, use natural grey and chromatic when you define you ICC profile, and use Highest - fine precision photographs. That gives about 10% larger colour space.
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Rune Stenseth