I rode that stretch daily for a year during rush hour and did not once have a problem. Rain. Fog. Sleet. No worries.
The blue lanes help.
In general, when I'm in a bike lane where a car might turn right into me, here's what I do:
Ride in the bike lane, but position myself so I'm next to or just ahead of the front quarter panel of the car to my left (which may or may not be turning right). I look at the driver.
If they're on their cell phone or blackberry (even more frightening than cell phones), I have been known to (very) occasionally knock gently on their window or windshield and wave "hi" in a very friendly, non-confrontational way if they look particularly deep in thought. This has led to people slamming on their brakes before, so if you try this while moving, mind you don't hit that giant SUV mirror.
However, I find that simply looking at the driver is usually enough to get people's attention -- must be some sort of genetically hard-wired threat indicator.
Then ride at the speed of traffic. Not faster. Not slower. At the speed of traffic. You can accelerate or slow down AFTER you get through there.
That blue turn lane on Broadway isn't too bad, IMO. However, having to cross a lane of congested and slowing traffic to get into it definitely requires me to accelerate to the speed of traffic and position myself in the lane.
Timidity is not your friend. Be assertive -- don't cut someone off, but if the best time to get over is 200 yards before the blue lane, then hop in there and pedal like crazy.
Why do I do all this? Most of it is second-nature to me now. It's habit. Do I have to do it? Naw. I could blow full steam through a light in my legally protected lane. But some motorists are distracted, just got into a fight with their wife, hate their boss, learned their mom has cancer, are dreaming about their wedding, or whatever. And frankly, I don't want to deal with their Yukon parked on my sternum.
Besides, the knocking on the window thing is kind of an adventure for me -- it's good bike-handling practice. And it makes me feel like a rebel because it sometimes freaks out the country mice from the suburbs who fear the "big city" and all its inhabitants. *knock*knock* "Hi there!" *big*smile*
I dunno. *shrugs* A lot of this is second nature now. I don't even think about it on the road. But it's interesting to see people's questions and comments in the forum because it gets me thinking about what I do and why I do it. Which is fun, because it's all about me. Me me me. Ha! *snort*