I would appreciate some strategies from the experts. I am trying to get my wife LGA-BNA-LGA in two weekends' time to meet her new niece - assuming the young lady has the good grace to arrive by then .

Pricing out leaving on AA1551 on Friday 2/6 and returning on AA1452 on 2/8 comes back with $500+ for an H class fare. Both the availability tool and an eyeball of the seat map suggest there are beaucoup de seats available, and the tool tells me that the cheaper fare buckets have not sold out. Searching by price gives limited improvement (L and V fares, but routed via ORD and saving only ~$100). So if there are lots of seats available and the cheaper buckets have not sold out, why does aa.com give me a relatively expensive H class fare?? Is this just the vagaries of yield management?? And does anyone have any ideas to get a cheaper fare, other than bide my time and wait for American to let the price drop if the seats aren't selling fast enough??