The way around this would be to shoot a "Bias" that's actually as Dark Flat/Flat Dark.
It's what I do with the ASIAIR with my ASI294MC Pro camera (cooled to 0°C, gain 121).
That way I have (NOTE: I do this in Live Mode in the ASIAIR since I do Live Stacking for EAA):
Flat frame done with a 5 second exposure, Stack of 20 (with my light source this puts the AVG AD?U at around 27000 - 28000).
Dark Flat/Flat Dark - done using the "Bias" frame tool - with a 5 second exposure, stack of 20 (I also done with a stack of 50).
Dark - exposure to match Lights (so one at 5, 10, 30 and 60 seconds), Stack of 20.
So for my Light, its either 5, 10, 30 or 60 second exposure (usually 30 seconds for me with my setup). I usually let it run for 10 minutes on any particular target.