Hey, did you ever figure out this problem?
I have the same problem as you, going on for over a year.. SC-P600. The printer is seriously pissing me off and I'm almost about to get rid of it, as I have tried everything as well. Different machines, different drivers, I have tried Mirage print, lightroom, photoshop.. The funny thing is that I the colours come out correctly while using the Matte black ink. With Mirage print i set the white balance to around +20 and I get something that looks like the correct colors, but some shades still have this green cast that I can't get rid off.
To sum up my problems: when I'm printing with the correct profiles with photo black ink I get a very cold image, not a colour cast like some ink is clogged, just a very cold/greenish looking image, as if the white balance is off.