My understanding is that Dr. Robert Powell has probably done more LAP-BANDs in the Dallas area than anyone else. He is not affiliated with AIGB ... his staff handles the insurance approval process from start to finish, and his aftercare program has a great reputation (critical to your long-term success).
Other options in the area: Dr. David Kim (North Richland Hills) and Dr. Nick Nicholson. All of these guys have phenomenal reputations and I'm told very good outcomes.
These are some good options -- look into each of them and see which one(s) might take your insurance.
Good luck!