Update:
It may not have been Avast's .dll after all. I just found out yesterday that one of my 2 RAM modules was defective; it's possible, I'd even say highly likely, that that caused all those browser crashes and Bluescreens. I removed it yesterday and so far I haven't had any more crashes. It's only been a day so far, so I can't be 100% sure, but I'll let you know if my browser starts crashing again.