I think you're exactly right. It's the initial draw at startup. I actually had a great conversation with one of the guys over at Xenon Depot this afternoon. He said that for BMW's that are this new, he always recommends HID kits that come with relays to wire directly to the power terminal in the engine bay. That way, the power draw is not on the factory wiring at all. Here is exactly what he recommended:
This HID kit (Extremely low 4.5A startup draw):
http://www.xenondepot.com/H7-HID-Kit...ID-p/xt-h7.htm
This Error Fix:
http://www.xenondepot.com/HID-Low-Be...Fix-p/rfix.htm
He says if you order both of them, you don't require any sort of capacitor. Their ballasts have built-in EMI filters so it will not interfere with wiring or reception of any other signals.
He thinks the heavy draw at startup is exactly what's causing the "Door ajar" error. Car has nothing else to blame for the initial spike in power loss, so it resorts to the last thing it knew of that drew power.
I looked up the Kensun ballasts on their website and they say that their ballasts have a 20A startup. Woah.
I will figure this out.