Integrated lights are a problem when something goes wrong with them, especially few years down the road when spare parts are nowhere to be had. Non-integrated you just chuck out and buy the new one for ten twenty or whatever dollars and you are OK again. I once suggested the integrated idea here and was put down for it and I have to say, I agree with the critics of it.
As for lights, no matter what you do, that kind of situation that happened twice to OP is still on the books. Happened to me once when 18 yrs old, in full daylight, I escaped pretty well unharmed, bike ended up on the vehicle front wheel pretty well destroyed, I flew over its hood and ended up rolling down the road curled up like a hedgehog. In those days, I rode with toe clips and so was free from the bike in no time, no idea what would happen if I was clipless like you all are nowadays.
Problem is the view angle the driver sees you. You ride on the side of the road and the drivers making left turn against you see you (if they do see you) against the road side where you sort of blend in. Besides car drivers typically scan the road without looking for any smaller details (like bikes) which are typically too much on the road side to be noticed. You should still do defensive riding even with good lights, rely only on eye contact which means not maintaining high speeds when you are close to home on town streets.