Rental pricing can sometimes be strange and often doesn't follow any rhyme or reason. We always recommend that our customers wishing to extend, price it out as an extension of their current contract, as well as a brand new rental if they don't mind returning and checking beginning a new contract.
It sounds like the latter approach may work best for you here, but keep in mind that you will need to return to the renting location to close out your current contract and then open a new contract. Also note that while they may let you keep the same vehicle, they will note the fuel level at return, so make sure that it's full so you don't get charged a refueling fee.