Searching the web I didn't find any solution to the problem. Epsons standard response seems to be "replace the ink supply assembly", which is a major part of the printer.
I suspect the problem lies in the black ink switch. After using the printer for years and maybe not switching black inks very often, there may be an ink build up on the "piston" that blocks the black line not in use. When switching from PK to MK (or MK to PK) the piston won't seal the ink line and the printer tries to keep the positive pressure. The black ink will then be pushed through the head, drops will hang under it until caught by the paper and give drops/streaks mainly at the edges of the paper. This is just my theory, and I guess the problem could be ink build up in the dampers as well.
Here's how I dealt with it. I haven't used PK a lot since but it seems to be working again, no leaks and no streaks on prints;
First I did the usual cleaning (bottom of printhead, capping station) with no luck. I also cleaned the ink and air connections for the black carts.
Then I made two cleaning carts (MK and PK) and filled them with distilled water and about 30% isopropanol. ( See
http://m.youtube.com/watch?v=hTbnlJgxMV8 for one way of doing it, requires a resetter and an OEM chip with at least 15% remaining). I switched PK to MK and back a few times to fill the lines with cleaning solution. Then I let the printer sit for more than a week (not a quick fix!). Once or twice a day I printed an A4 filled with black through QTR using only the black channel, this way no color ink was wasted. I also switched between MK and PK so that both channels were used, MK was selected most of the time though. If my theory is correct keeping the MK line open will let the ink build up resolve from the piston, and then make a tight seal when selecting PK.
Finally after more than a week when switching to PK the prints got darker and then lighter again, showing that something may have been resolved. I kept the cleaning solution for a few more days and then changed to MK and PK ink cartridges. Now it prints OK with both MK and PK with no leaks. The trick seemed to be giving the isopropanol enough time to work.
Good luck!