You might want to consider renting through a private owner - the price would be more reasonable.
http://thevillages4rent.com/ has villas for rent, with pictures and prices. We used to rent out our patio villa, and it does tend to be a little more sociable, in my opinion, with the lanai on the front. If you really like privacy, I imagine the courtyard villas are nice. March is in high demand, so you'll need to make your reservation soon. Good luck.