Gee, that banding shouldn't be there. I think you could try a different print setting - use "more passes" only. Sometimes that helps.
Here is info from an HP Document about the issues you have:
"Check that the paper type you have loaded corresponds to the paper type selected in the front panel and in your software. To check on the front panel, use the View loaded paper key.
Check that you are using appropriate print-quality settings for your purposes (see Printing). In some cases, you can overcome a print-quality problem merely by selecting a higher print-quality level. For instance, if you have set the Print Quality slider to Speed, try setting it to Quality; if you have already set it to Quality, try selecting custom options and then More Passes. If you change the print-quality settings, you may wish to reprint your job at this point in case the problem has been solved.
Print the Image Diagnostics Print. See The Image Diagnostics Printimage diagnostics print .
If the printheads are working correctly, go to the front panel and press the View loaded paper key to see the paper advance calibration status. If the status is RECOMMENDED, you should perform paper advance calibration: see Recalibrate the paper advance."
Paper advance calibration should have fixed that issue.
Maybe run another diagnostic print on Gloss or semi-gloss paper and see if you have an issue with any of the black heads. My guess is that you still have some printhead issues that should be cleaned and/or replaced.
Oddly enough, those small banding marks can disappear by just changing the print settings to either better or less - just do the opposite of what you're doing now.
Did you put new print heads and new inks in that thing? Recently expired printheads should be okay....
-Mark