Clark,
This can actually happen unfortunately, with this model. I switched the PBK to MBK and it took up to 7 cleanings to get that channel to fire properly; this was after not using the printer for a few weeks. Just the way the model is set for some reason.
There is only 1 print head in the printer (like all Epson models) and around 1000 nozzles per color (those VERY tiny holes where the ink droplets come out of). This is why you see the option in maintenance for "nozzle check" available so it can check them (mainly testing each color channel). If you have line breaks in the nozzle print, this is because those nozzles are clogged/not firing properly.
I've seen this issue happen more with the PBK/MBK channels since they share the same line, but just purges the one black to switch to the order (based on media type).
So you may have to do a handful of cleanings to get it pushed through. The one option to help it vs the multiple cleanings that do every color, is make a small box (around 1"x1") and fill it in with the darkest black you can select. Than print it on plain paper (or matte), so you can use as much of the feeding options to change sides and turn over to use those sides. Keep the media type the same even though it may be a different paper type, it will be fine. You're just trying to help the printer push the ink through. Do another nozzle check to see if it helped at all. At times, the nozzle check will attempt to check all colors (as well as the cleaning), but the issue may help resolve the black, but another color may get slightly affected during the process and do another cleaning to help resolve that.
Not saying this will fix it completely, but a method of trying so you don't use up more of the colors than needed.