I'm just putting some notes here to recap for myself. (There are several Kz550 threads going right now.) Let me know if any of this is wrong.
No compression test numbers yet.
All valve clearances were checked and re-shimmed.
Factory Ignition with Dyna 2.2 ohm coils.
Short free-flowing exhaust.
Custom, short, four-gang filter box. (Looks to be a pleated paper element.) Nice fiber work.
K&L needles set to 3rd clip.
Stock main.
Stock pilot.
Air screw setting?
Fuel level set on all four? Did #4 stop leaking?
Plugs look rich, but about the same across all four. #4 may be lighter on the insulator, but lighting was varied.
(I try to photo all four next to each other at the same time so the lighting is not a variable.)
The video does not sound that bad, actually. Is it misfiring there, or is that with it running normal?
Did you do a water test to check for misfire, or is the pipe (#4) so cold you can just grab it?
I think the rich plugs are from being on the 3rd clip position (counted from top), as I've found that to be a little much. But 2nd clip position would be too lean. There is a shimming needle page on my site. I would try a .6mm to .8mm shim. But that is not the dropping-out cylinder problem.
Is it for sure only one cylinder dropping out when hot?
If so, my first reaction would be to check the valve clearance on that cylinder. But you've done that.
I still think a compression test would be a good idea just in case there is something strange on that cylinder, but the odds are lower if it is running ok before the cylinder drops out.
So next is ignition. If two cylinders were dropping, in pairs 1-4 or 2-3, I would suggest swapping coils around to decide if it's a coil or the Dyna S. The Dyna S can be sensitive to voltage, so I would try to measure the voltage on the battery and the positive voltage going to the Dyna S itself while running and misfiring. The Dyna S grounds through the motor, so does the starter, so the ground should be ok.
How long do you ride before the cylinder(s) cut out? Does it always cut out at that distance or time now? Or is it for sure, more random?