Albert,in your post #6 you wrote that you get the doubling while printing the K alone. Is this with any other units on impression? This should help at least narrow down the problem.
For example,if you had a bad transfer gripper between the 2nd and 3rd unit,the black would double,but not until after it hit the 3rd unit blanket. If you are getting a doubling with just the second unit on impression,it would rule out alot of other variables. If it is doing it with just that unit on impression,the problem is isolated to that unit alone. I would think blanket or plate movement somehow.
This is a long shot,but do you have to move the K image down as you run to keep the black in register? You might want to make sure the bolts that hold your circumferential adjustment are tight. I have seen this cause the fit to move,not double,but I suppose in an extreme case it might double.
You also mentioned that you have the unit packed correctly. Did you use a packing gauge on it? I've seen blankets marked with the wrong thickness stamped on them,so I always use a gauge. I have also had the blanket/ packing swell up from wash up solution/water getting under them. This of coarse will throw out your squeeze.
Just throwing a few ideas out there.