Thanks for posting screenshots! These help.
A few things are happening in the workflow here.
First. You are using a third-party ICC on a third-party paper (not what we built the inks to match, we build the inks to match Epson papers with Epson ICCs) with VM and VLM inks.
Second. You are printing at 720dpi which will starve the print of ink. This Inkpress profile requires 1440x720dpi as a minimum (with Finest Detail on).
Third: Your inks are most likely in need of agitation if they have been sitting that long. Pull the carts, shake them gently, put them back in and run 2-3 maintenance cleanings to get the fresh agitated pigment through the dampers and through the heads.
Fourth: What you will need to do is get a custom profile (or build a custom profile) and use that profile to Soft-Proof with on your screen before printing. Ideally you will build this profile at maximum quality of 2880x1440 dpi (make sure not to turn highspeed on but make sure Finest Detail IS turned on.)
That custom profile will actually work very respectably on a vast array of matte papers that are similar to the inkpress (better than using profiles that were made on other printers, with other inks even though they were made for whatever specific paper you are printing on).
http://shop.inkjetmall.com/Custom-ICC-Profiles/ (or others out there online)