Every time my DH got transferred we had to do the packing. I have a girlfriend who has packed professionally. She showed me some of the tricks of the trade. They do label things very well. I would go ahead and let them do it. It would make life so much easier for you. Many things would be packed better than we could do it ourselves. The next three things you want to do, pack yourself and put in the car with you along with one sewing machine. Then you'll know where they are.
Possibly you could ask for one of the packers to be a woman. They usually pay better attention to details.