Tell everyone you know, in the most public way possible, what the name of the company is and what happened.
This is why I advise everyone, family and friends, to get a video camera and take CLOSE pictures of every man who carries stuff out of your house. Take close ups of them, and take close pictures of all the stuff coming out. If possible, have 2 cameras working all the time. Then have someone hold up that newspaper with the date on it, revolve around them and take pictures of each room you left. This is because, sadly, most houses left empty are immediately invaded by the homeless and neighborhood thugs that live way too near.
Then take the same pictures of your stuff coming OUT of the truck, with the same closeness of movers and possessions.
Plus pictures of the house you are moving into. Should it be rented, this will prove, by the newspaper, that the house had this or that flaw in it. Be sure to highlight each thing you want fixed or changed in the pictures.
And be sure to change the locks on the new house, every one of them.
I suspect that the best way to get reimbursed for this is a glare of publicity. Tell your friends in the old neighborhood and in the new one, tell what the name of the company is and what happened. Tell us...some of us might live near you, or have friends or family there, and remember, word of mouth is powerful.