Laura,
I definitely do not want to appear to be "picking on you" or anything like that, but your two situations support my position precisely. I also know that I am over simplifying this, but just trying to make the point that all "accidents" are avoidable.
In the first, you did not see the errant driver (until too late I imagine) because the street was busy. If the street was that busy were you moving at an appropriate speed for the circumstances? And I don't just mean relative to the speed limit. An appropriate speed would be one at which you have enough time to see and react to all of the possible problems.
In the second (again in heavy traffic), you point out the trap that we all tend to fall into. We can't leave an opening (an escape route) because some jamoke will jump in and fill it. I see this all the time. Unfortunately it is human nature to then "retaliate" by leaving too small of an opening for those miscreants to move in. But the irony is that by doing this you are only putting yourself in jeopardy, not the miscreants.
What is the downside to just backing off again? I know, you won't make good speed and get to where you are going quick enough. I think more bad things happen because we are all in such a rush than for any other single reason.
Leaving an escape route isn't just about staying 3-4 seconds back from the car in front. It's also about intentionally leaving openings in the adjacent lanes to allow evasive moves in a lateral direction too.