Thanks for all this Doug. I think I understand most of what you say, though I'm not a colour management pro, by any means!
I'll increase the thickness setting as you suggest, but fwiw, I printed the profile target twice, once with the printer's onboard LCD panel media selected as PLU260 (the profile attached previously) then I printed it with the paper selector set to 'Baryta', which is presumable thicker(?) - I'm attaching this here.
Maybe this makes no difference, but you can illuminate that. Annoyingly Epson allows you to select 'Legacy Platine' on the computer's printer driver, but not on the printer itself - there is no Legacy Platine option on the LCD, so I used PLU260 media profile, which is often the go-to for quality 3rd party papers. The 2nd iteration using 'Baryta' media profile is maybe a better /thicker alternative?
(Not sure which of the 2 media selector options over-rides the other. Maybe the Workstation driver over-rides the printer, and these profiles are identical? Or vice-versa. Its confusing, and Epson need to sort it out)
Thanks