I managed to move my 44" Z3200 from San Francisco to Hawaii without incident. It was a little nerve wracking, as it had to be sealed up in a shipping container for 9 days, but I wound up without a single problem as a result. There wasn't even any head clogging after being shut off that long.
I had saved the foam ends from the original packing material, and used those to secure it onto a piece of plywood with the same footprint as the printer. I lashed them on with lots of stretch wrap. Mine also had to go down a flight of stairs first, and I don't know if it really mattered, but I carried it down with the carriage parking end on the downhill side. I used blue painter's tape to secure the carriage, so there was no chance of it moving in transit.
I would suggest that you clean the cover you mention. The simplest method is to tell the printer that you want to replace a printhead, then clean the cover while the carriage is in the position to do the head replacement. This has some additional baggage associated with it, in that the printer will then declare all of your calibrations obsolete, and I think it will even ask for a printhead alignment. I haven't done that in a while, so I can't remember that part clearly. What I do, though, is to turn the switch in the back off while the carriage is in motion. It is helpful to clean the wipers under the cover, too, and they are usually exposed when you first turn the printer off. I catch it, to turn it off, when it is sending the carriage all the way to the left as it is loading a new sheet of paper. It doesn't behave the same way when loading a roll, so tell it you are loading a sheet and try to hit the switch when the carriage is not behind the center support bar. If you miss, you will have another opportunity. When you first shut it off, you will have an opportunity to clean the inner parts with a coffee filter. To get the carriage in a better spot, and to get the cover to slide closed if it isn't already, turn the printer back on. After a couple of minutes, the carriage will move very slowly into position and the cover will close, at which point you can turn the printer off again and finish the job. That cover is often fully covered in excess ink. I haven't had any issues with this process, and have to do it whenever I get random drops of ink on my prints.
Best of luck with your move.
