For color we recommend using a custom ICC profile for non-Epson media. Our own ICC profiles which we produce use only one of the Epson media settings for matte and one for glossy/baryta - no matter what the matte or non-matte media is.
An Epson media setting is actually a CLUT (color lookup table). Selecting a media setting actually changes the amount of ink coming out of the print heads. It is rather “serious business”. We select Ultra Premium Presentation Matte when we make ICC profiles for any matte paper including Type 2. We select Ultra Premium Photo Paper Lustre when we make ICC profiles for non-matte papers such as the baryta surface of Type 5. We find that these two media settings produce the best linearizations.
For Piezography we suggest always a media specific curve.