i dont know about on jv4's, but on our jv 3's and 33's there are two little screws on the front of the carriage, if you tighten them up it raise's the head higher off the paper. you get better quality from having carriage set to thin, but you also run a higher risk of head strikes and messing up your heads. We have all of our carriages set to thick at the moment, and have for as long as I can remember. There is also some kind of set-up you have to do threw the configuration tree on the panel on the mimaki, but all of that was already set when I started working here a few years ago. It just lines the print heads up correctly so they adjust for the difference in the gaps.
The carriages HAVE been known to, over time, start to droop a little and start causing head strikes in dang near everything we do. Either the screws will become loose from being in near constant motion, or the belt that the carriage moves on starts to get a little worn out and start sagging. I'm not sure how to tighten up the belt, but I know that in 8 years of printing with our JV3's we have never had to actually REPLACE the belt.
To see if your head is sagging too much, just watch it go back and fourth as it prints, if it looks too close to the paper, or if it is clipping the little metal sliders that hold the paper in place, you need to make it a little higher.