Having used car shippers in the past, they will not give you dates certain for pick up and delivery. They usually will get close. Renting a U-haul truck trailer will be expensive as they charge mileage on the moving van. Have you tried to borrow a pick up and trailer from someone in your region?
Along this line, another consideration would be to get a group of drivers from your area, and rent one Car Hauler (can't remember how many cars they carry 8 - 10), to deliver and return all of your cars on one truck load. Several groups of drivers have done this. Not sure how much the cost was......maybe one of the people that have done this will post the details and costs associated with the Truck Load move.