If what you are describing is what I think is call 'banding' in the direction of the print head, then this is what I did to mitigate the problem on my Epson 7800:
Set the Print Quality to Maximum (Setting 5, 2880), and it's okay to leave High Speed On (turning if off made no difference)
I tried a Power Clean, tried using Piezo Flush to clean the Cap Station, Wiper Blade, and Print Head, tried printing purge files, played with the paper feed adjustment, none of that worked for me.
I am missing several 'small lines' in the nozzle test pattern too, but it doesn't appear to be a problem, i.e. banding is not an issue for me, until quite a few nozzles are missing... at that point I do a nozzle clean from the printer itself and banding is gone.