I think you would do best to rent the van the entire time. Normally on one-way rentals you get charged the daily rate plus a drop off charge. With some companies the drop off charge is calculated by the mile (ie. 20 cents a mile) Coming from Nebraska this could be a chunk of change! Be sure you understand the drop off charges BOTH ways if you decide on one-way rentals.
Also, be sure your rental will allow you to take the van to Florida. I had a rental from one of those insurance places that would not allow me to take it out of the state.