Just rent for the minimum then negotiate
I just rented an apartment through AirBnB and selected that service for the sole reason of earning Delta miles. Our intent was to rent for close to two months but the one apartment was rented for a weekend so we only reserved for the first week or so. At the conclusion of that rental we explained that we wanted to rent for two more weeks and the owner was more than willing to bypass Airbnb and do a cash transaction for the extra rental. They happened to have another apartment in the same home so we just moved there for a short time and then moved back in to the original one. I would suggest you rent for the minimum stay and then when you get the owner's contact information see if they will rent the rest of your stay outside of Airbnb.