The media settings definitely have an important impact on the amount of ink applied to the paper. As a test, I've printed out a 1728 patch target on Epson Premium Luster using a few different media settings. Its pretty different, even when using the HW Semi-Gloss Photo Paper and Semi-Gloss Photo Paper. I haven't yet tried the Photo Paper Plus settings, but nailing the optimal media setting is crucial to building an effective output profile. For instance, the HW setting gave me significantly less color than the Semi_gloss Photo setting.
I look forward to more experience with this printer, but it definitely takes a bit of brute force to get decent color. The software is bloody dreadful!