ok, quick recap.
1) is any of the radio equipment aftermarket? i think you mentioned that the headunit is, right?
2) only does this when in drive, not when in neutral or park, right?
3) when it shuts down, what is on, electrical wise?
4) do you have a tune on the car?
it seems to me that something is drawing an extreme amount of power from the battery when the trans is in gear. how long ago did it start doing this, and have you added any mods since then, or recently enough to when it started messing up?
have you checked the TPS yet? (TPS = Throttle Position Sensor). if this starts acting up, it can screw up the amount of air that should be entering the engine and cause the idle to drop too much, which with all the other accessories you have on could cause your car to stall.
check all the bulbs on the car, mainly exterior ones, make sure there isnt any rust or anything that could be causing something to arc and draw more power than it should.
go out during the night and find a dark area, pop open the hood, and see if you see any fireworks around the coils. coils could be going back (not likely, but a possibility) and drawing too much power. the reason i say go out during the night to a dark area is because this way, you can visibly see sparks coming from the coil packs, whereas any light would inhibit your ability to do so easily.
hopes this helps.