A few suggestions:
Consider a one or two-bedroom unit at one of the condotels. Villas at Banyan Bay, all two bedrooms, are very nice and have jacuzzis. Banana Beach, especially the seafront units, are attractive and a great value. The Palms also has nice apartments.
If money is no object, the villas at Cayo Espanto (on a tiny private island on the back island of Ambergris) are very luxe, and you get meals delivered to your house and your own personal butler.
Mata Chica's cabanas are beautiful ... though it seems like Mata Chica is closed in September.
You might also look at renting a private vacation home. Quite a few have ads here on the AmbergrisCaye.com site.