The nozzle checks are too small for me to judge them very well. However, from what I do see, some missing nozzles appear to be "moving" from check to check which suggests that some air has been introduced into the system. This is not an actual clog, just that a pocket of air reaches the nozzles as it ejects the ink.
I think you have got, for the most part, piezoflush down to the nozzles. If you have real clogs, (I can't tell from your attached image), you may have to leave the piezoflush in for a long time. I did an experiment with an old clogged R2880. The ink was so dried in places that even the nipples that poke into the carts had clogged ports. These clogs would not free up even with piezoflush carts sitting on them for several days. I never did find out how long I'd have to let it sit before the clog would finally dissolve out, but I'm sure it would eventually.
Do you have any old carts with battery chips? If so, swap the battery style chips to your piezoflush carts and reset the battery chips. Then you can refill the carts with piezoflush and do several repeated ink charge cycles. Be aware, this will use a lot of piezoflush. You're probably better off doing one more ink charge then letting it sit for a week or so. NOTE: you should also do matte/gloss black ink change to get piezoflush through the matte black lines.
Physically emptying the carts will not make the cart think it's empty. The printer keeps track of how much ink is used during printing and cleaning cycles and deducts the amount of ink from the chip. If you physically empty the cart, the chip will not be updated with this information. This is a huge disadvantage to the autoreset chips.
Here's one other thing you can try. I already asked Walker if this would work and he said it would, but the timing has to be right. Turn the printer on and pull the plug just at the point when the head sits over the capping station. I presume you can watch and see when it begins to pull ink through the waste lines. If you stop it right here, I believe you can pull the waste lines out of the waste container and use a syringe to manually apply a vacuum to the print head. This way you could simulate an ink charge without the headache of the printer telling you it can't be done because there's not enough ink.
Again, if the clogs are really bad, it may have to sit with piezoflush for a week or more before the dried ink inside the head is softened up enough to pull through.