Gulf State Park in Alabama is one of the largest public projects to be funded through the Deepwater Horizon settlement. Many more are coming.   The Lodge at Gulf State Park is built directly into the dunes, so when you walk from the parking lot into the spacious lobby, you’re looking straight through the glass back wall of the hotel, across a stretch of white-sand beach, and out into the seemingly endless Gulf of Mexico. For Alabama, whose precious few miles of beaches all but carry the state’s tourism economy, this was the essential goal of the Gulf State Park Enhancement Project: A view of the sea for visitors and,…