I think I see a possible general process now. Wind shear over the crater from the typical wind direction creating two main vortices, with the wind descending along the crater mid line parallel to the wind direction. The longitudinal dunes would tend to form away from the mid line where the vortices are ascending and perhaps colliding with auxillary, less ordered marginal vortices. The longitudinal dunes here are oriented right toward the highest part of the rim because it causes the wind to "stack up" and descend into the crater. (I had been thinking the wind would ascend along the mid line from 2 main vortices, so you could only get one main longitudinal dune. Perhaps the rim asymmetry causes this, but I now suspect that this is the general case even for a symmetric crater. Wind would always stack up on the downwind rim and set up 2 main vortices with medial descent. These dunes are a great chronicle of past wind conditions, if you knew how to read them (not me). Maybe I'm just blowing smoke here, but if I did smoke, I'd blow some over a fake crater to see what happens.