Epson RX595 prints "wet" on non epson paper

When I print a photo on non-epson paper from my Epson RX595, the photo looks wet and smears when touched. When I print on epson paper, it prints fine. Kodak and HP paper give the "wet" result. I have contacted Epson support and done all of the typical maintenance (clean the nozzles, etc.) with no success. Epson says I should be able to print on any paper, but obviously this is not true in my case. Just wondering if anyone else has had this problem or knows of a solution.