Pack your stuff yourselves, that way you're sure that its well protected. Buy used big boxes (from grocery stores, etc). Store and pack all of your things in there, from plates to clothing. Label them with a code or something that only you can understand, so the hakot guys would not know what is in it, just a precaution.
Instruct them to separate the fragile from the general stuff. Have one family member supervise the guys inside the house, and another family member on the truck. You list down each box as it goes out if your house.
Reverse procedure when you arrive at destination.
I did that, it wasn't easy. But then again, who said moving house WAS easy.