I suggest buying some Epson Exhibition Fiber paper, similar thickness, probably a little less flat in my experience. If you have the same problem, Epson tech support will be forced to cooperate, I'd think.
Also, just FYI, I'm having no problems with Canson or Ilford baryta papers on my P600. Normal platen gap, paper thickness set to 5, high speed turned off. I did have "tail end" of paper strikes at default "3" paper thickness.
Rand