I would agree. If you wanted Besh, the one that might work best is Domenica. I've had some great food there. Relatively casual.
I used to work for Besh....I'm famous among some of his former employees for an incident that happened at Artesia restaurant when we both worked for Vickie Bailey who owned the restaurant. Another restaurant that I highly recommend in the quarter is Olivier's across from the House of Blues on Decatur. It's a moderately priced authentic Creole Restaurant. It used to be in Gentilly, but moved to the quarter.
Very few places have dress codes that are strict. The economy is bad enough that no one will turn away business because people aren't dressed properly. For the kind of food they serve there...shorts and flip flops are out of place. I wouldn't even wear a Polo shirt there.