At the risk of starting an argument, really, if you're going to be on the sidewalk, walk your bike. Cars don't expect you to be there. The driver in your most recent accident obviously didn't. I'm really glad you weren't hurt; being hit and thrown into potential traffic is my biggest winter commuting fear.

And on topic, the things I've learned from being hit are that drivers sometimes don't see me. I try to be as visible as I can, but my main strategy to avoid being hit again is to route my commute by bike trail as much as I can, even if it adds some miles.