Car rental pricing is often not logical. The reasons for this are many, and sometimes even varying your pickup and/or return times can change the price by tens or even hundreds of dollars, but asking customer-facing rental company employees for an explanation is almost always an exercise in frustration. A couple of additional comments:

1. Rental pricing can change often. We'd recommend making separate reservations--one for the entire rental period, and then, additional separate rentals for however it prices out lowest. Then track all those rentals with AutoSlash. May is almost half a year away which in car rental terms is a long time. It's almost a certainty that prices will change in the coming months.

2. You will absolutely have to return to the airport to close out one rental and sign a contract for the next one if you have multiple rentals. You may be able to keep the same vehicle, but you will have to physically return to take care of the paperwork. Anyone who tells you different is either misinformed or misleading you.