My biggest concern is that you wouldn't fill the whole cavity, so it'd be a pointless waste of money. The only way to insulate properly, would be to pull the tub.
How come the contractor's not there, repairing everything free of charge? Or another contractor there, reapairing things, and the first guy getting sued to pay for it? The uninsulated space behind the tub, for one, is a code violation - pretty open & shut case.