First, I don't understand why you've called this a focus issue. Is there something going on you didn't mention? I have no idea what's going on from your description and with no examples posted.
Since you're coming up to the end of the warranty, you need to get on this fast.
I'd run an indoor test where you can control the lighting, so it's definitely the same, frame by frame.
Put the camera on a tripod too, so you know it's aimed at the same place all the time, to ensure no lighting change shot to shot.
I'd set the meter to manual initially, and the WB as well. Shoot in bursts of various lengths, repeating that a number of times and see what the results are. Then do the same with the meter set to the mode you've been using if not manual. Do the same with the WB.
If the results vary, call Nikon and get your D4 into them pronto, so it's warranty work.