About last minute packing - some of that will have to be done. And you likely won't do worse than my parents. They moved last summer and were told that the moving company they hired would do the packing when they arrived, so that it would be insured on the truck. However, when the guys got there, they said no, they never pack. They had no boxes or anything. Needless to say there were some panicky moments. Mom and Dad had nothing ready, and a whole bunch of moving guys waiting to load the truck. So while the moving guys loaded the furniture, mom and dad and the kids ran around like mad throwing anything and everything into whatever boxes they could come up with. When they got to the new house, they discovered boxes with things like "coffee filters, two hangars, a single sock, the toaster, and a couch cushion" Mom said at least all the stress of packing was confined to a few hours. And they made it to the new house with all their stuff, and nothing broke.
Hope your move goes more smoothly than that!