I don't knwo how your printer works, but we use a Roland here. I usually make sure that any black I use is set to RGB. Have you contected your supplier or the product manufacturer to see if they have a profile for you?
Yes - we are using a material supplied by flex europa - they don't have a colour profile.
We are printing with a mutoh 1614 the bigger brother of the printer with problems and thats fine. And so is the roland - same material
Have tried various profiles and altered the black setting - it almost seems like a static problem between the machine and the media - i.e it seems to be a problem specifically with the mutoh 1314 (works fine on all other media).
If you say you have tried various profiles then what I would expect from that is different colour strengths. If you're still having a ghosting effect then maybe there's a compatibility issue with the media on the printer?
At risk of stating the obvious... using manufacturer's profiles is better than not using a manufacturer's profile, most of the time. But if you want the job done right, do it yourself. (Here's a comparison between a home grown profile and the one a leading distributor supplies with its canvas The Result - simply a better print | Hudson)
If you print a Grainger rainbow you'll be able to see where/why ghosting is occurring if the colour lightens as its fading into shadow. (useful resource for test images here test images for printing and lens resolution) There's no good quick fix - get the ink limits right, and produce a quality ICC profile to finish the job.