Mixing is indeed a problem of dampers and mainly the K valve, just as infamous PK streaks. I recently had a similar issue and after manual damper/valve cleaning some mixing unfortunately still appeared. Here are 2 more remedies that can mitigate the problem: (1) try to cycle PK>MK>PK... few times, (2) power off the printer when not in use as it reduces the printer idle + ink pressurization time.
In case of entire colors missing - did you prime the dampers and K valve after the cleaning?
Now few steps to do it...I'm assuming you have the upper housing off, the whole ink system with dampers and K valve disconnected from printhead. Now the priming can be easily done, especially if you have refillable carts.
You just need to disconnect pressurization hose (left side of the cart ) from air pump, plug a bigger syringe (50ml or so) to that nozzle, using a piece of soft tubing and whatever adapters you need to have a tight connection. Apply some pressure using it (push in some 10-20ml air...gently); this acts in similar way as actual pump and now valves in dampers can operate as they should. Take another syringe (normal tip, no adapters, 10ml or similar size) and gently attach it to one of the damper output ports; syringe tip must not go in, just touch the gasket. Pull few ml of ink until no bubbles come out. If you pull more, you can return it to the respective cart / bottle. Repeat for all channels, push in more air if ink stops flowing. Additionally for K ink, manually rotate the servo of MK/PK valve (small tube connected to opposite motor shaft makes it easy) few times to make sure both lines and dampers are primed.
You can also use this moment to (gently!) push some cleaning fluid to p.head ports. Use syringe+tube, apply low force and don't use very small syringes as they can induce much higher pressure.
In my case, after the re-assembly, a single, normal cleaning cycle produced clean nozzle check (well, as clean as my print head allows
