Although Ihave never heard of a business of unloading rental trucks... as the concept of the rental truck is Do It Yourself, I can understand from the zip you are coming from 28412 to where you are going to 12571 it would be a savings to make the trip in a rental. I am going to refer a local moving company to you that has moved a few of my clients a short distance. They are not a big name company and may be up for the job. Can't hurt to ask. They have been very reasonable in their rates for each person I have refered.
The phone number of the moving company is 914-320-8604... Tell them John Durso from Realty Executives refered to you.