Blind Spots from Window Socks - near miss

Ladies, I would like your thoughts/suggestions.
Yesterday I found myself part of a situation that I have no doubt happens many times every day, but it was horrible and had the capacity to impact on so many lives.
I drive a VE commodore wagon. The blind spots are crazy to start with, but with 2 munchkins I also have the fitted window 'socks' on the rear windows. It means that at certain times during the day (when the sun is in specific spots) the drivers side rear window becomes part of the black spot.
I was pulling out onto a highway from a slip lane, 100km/h I looked, and looked, and looked, turned my head to look, looked in the mirrors, indicated (and had been indicating for a while etc) - I didn't see anyone next to me. Well, there was a motorbike next to me with a passenger on board.
I almost killed them. I didn't run into them, but that is only because they saw me. There were cars behind them, and cars infront of me, and people in my car - it could have ended so horribly and affected so many lives. I feel sick just thinking about it.
The motorcyclist was furious (and rightfully so). I just didn't see them. I am a cautious, alert, aware person. I work in a safety related job - I get the importance of getting home safely.
This has really rocked me, and felt so guilty, and like an absolute idiot.
My windows are tinted - any darker and I don't think it would be legal.
Removing the window socks isn't ideal for my kids - we spend a lot of time in the car and they hate the sun hitting them.
Do you know of any other solutions?
I've gone as far as thinking about how the motorcyclists were dressed - all black, all black bike, no lights on (it was 2pm so not dark or anything). We wear high-vis in our industry to ensure we're seen. I don't know. I just feel like this has the potential to occur again unless I come up with a better idea.
I'm losing sleep over the flashbacks - so I thought I'd put it out there.