Hi Julian, hope in the months since you posted this you sorted things out. In case you didn't (or for others this might help), I suspect you most likely have ink residue buildup on the right-side servicing station that's getting onto the carriage and heads and then dragging it across on the edge of the paper. The best analogy for this is the cat sh*t on the floor and the Roomba tried to clean it up
On the printer menu select the option to replace printheads. When the carriage moves over and it says to open the lid, turn off the power on the printer (rear switch by power cord). Then you can freely slide the carriage to the left and see into the right-side service area. You'll probably see gunk "everywhere". You want to wipe that up as much as you can. A bit messy but with patience you'll get it good enough. It doesn't need to be spotless (impossible), just getting rid of excessive buildup.
You can make it a lot easier to see/access by removing the right-side cover off the printer. This will also let you move the position of the service / capping station for a more thorough cleaning.
Also wipe any buildup off the bottoms of the heads (carefully!) and the carriage edges. Also check closely around the paper rollers at the right side, etc. Just make sure there's no ink globs sitting anywhere.
Check the left-side area as well, but it should be nowhere near as bad. Just make sure a glob didn't fall off the carriage somewhere over there.
After it's cleaned up you shouldn't have any more streaks like this.
Some pics from my Z3100... showing the right side cover removed, then the ink sludge on the servicing / capping station, and then the capping station after it's been cleaned.
Cheers!