If there is black ink coming from the head (after this many cleanings with flush in all the lines), it is NOT the head electionics , but either the dampers or head manifold. Something is not getting cleaned by the flush because the flush just can't get to it because there is a block (above the head).
I assume your flush level has gone down a bit in the carts meaning the cleaning assembly (vacuum) is working. It should, because it's new.
Because you've tried it all, you have one more thing to check/test:
What we do periodically with this style head is pull it out, cover the top element (it has coper wires exposed) and manually flush with a small format flush kit over a cup or bowl. Sometimes we'll actually suck up in the opposite direction (from the head plate up through the manifold) in case anything is stuck in the manifold. Then we'll flush and make sure everything is out. Then we'll let it sit over the flush for a night. When manually purging these print-heads it's important to do it with as gentle a pressure as possible (not too hard!). You will most likely see black ink come out (and some colors). This is a purged channel.
Make sure you never get any liquid on the copper contacts where the ribbon cable goes in. Check for corrosion on the cable and head contacts, etc.
Put it all back together, make sure the dampers are aligned and that they aren't screwed in too tight.
Then do a few cleanings. Make sure you don't have back pressure. Doing the cleanings with the right cover off can help because you can also check that the cleaning vacuum pad is making connection with the head (no air gab) and that ink is going from the vacuum to the waste tank properly.