Sorry to be late to the party. FWIW - I had something similar going on with my 1204 a few months ago. Turned out to be the sensor that reads the encoder.
This comment might have saved me $5000 or more if I decided to just buy a new machine
I am being optimistic, but it might actually be the cause. Since last week we have been printing 14 hours a day on the loaner to get back caught up. I was convinced it was the main board because of it blowing all ink cards. And the tech was convinced it was a printhead because we had a few missing black. I didn't want to risk blowing more ink cartridges if it was the main board til I got caught up. So this morning I popped in the used cartridges I have been using (all under 50%) and sure enough my Mutoh fired right up. The test I wanted to do to convince the tech it wasn't the black was to print (in cmyk) 100% Y C M and watch it still shift. So I printed it and guess what?? Straight as an arrow with no shifting whatsoever. We cleaned the sensor right before we lost all cartridges so we never got to test it after the cleaning.
The head wasn't sitting on the station for some reason so my prints are still a little spotty, but I am soaking the heads now and will do a flush to clear that up. I should know in about a hour but I really think it might be fixed. We were going to order a new head and main board today to get over this issue once and for all.
if it is the case and I am good, and I ever make it to Ohio I owe you some beverages and a hug haha