If you've done all the HP-recommended steps and the ink carriage seems to slide easily with the printer off, there's one more step you can try, if you don't mind getting ink on your fingers.
With the printer door open and the cartridges out of the way, see if your printer has an inkjet wiper tray that sits under the cartridges on the right side of the printer. The tray should slide easily backward and forward, at right angles to the print carriage, with just a little hesitation when the wipers go under a scraper bar that sits behind the carriage.
If the tray feels sticky, ink may have accumulated in the tray's guide rails. (My c4385 had printed almost 9000 pages when this happened.) You can clean the rails with cotton swabs and rubbing alcohol (I used cotton balls, a hemostat, and cheap vodka). I didn't go nuts, just cleared where the moving parts slide. I was careful not to get alcohol anywhere where ink doesn't normally splash.
When you've got the tray moving smoothly, make sure you remove any stray cotton fluff, especially from the rubber wipers. Then close up the printer and print a test page (On the c4385 press the Cancel and Green buttons). This cleared up the issue for me.