Ok, been experimenting today and I have a little bit of an update.
Started off by trying the light box plugged directly into the battery with no dimmer.... No banding!
Next I plugged the light box directly into the ASIair port (running at 100%), without the dimmer attached.... No banding also!
Next I set the ASIair power output to 50%.... Banding returns. This was expected as the ASIair uses PWM to vary the power output to light boxes and dew heaters.
Following that I plugged the light box back into the battery and reconnected the included dimmer.... Banding was back again.
After a quick google search of the dimmer switch, I discovered that it also uses PWM to dim.
Obviously I am happy that I have discovered what is causing the banding issue, and I can indeed use the light box with t-shirts or pillowcases to dim it.... but the whole point of getting the light box was to make the task of taking flats simple.
So now I have another questions, does anyone know another way to dim LEDs without using PWM?