I agree that waiting in the center of the lane in the traffic stream helps, but many places similar to what the OP describes are indeed very problematic. I regularly cross a road that is 8 lanes wide + 2 center turn lanes + grassy median. And the green cycle on the cross streets is VERY short, with no pedestrian improvements or signals at all. From a standstill at the front of the lineup of cars, I can just barely clear the intersection before it hits red if I accelerate all-out. Motorists get very frustrated by these intersections, because only a few cars usually get to go per light cycle from the cross streets (and usually only 1 or 2 if they're behind me). I ALWAYS get passed in the middle of the intersection, or right after, and there is little I can do to prevent it. I find this kind of intersection is among the most dangerous places I ever ride, but I have to cross the big road somewhere because it's an enormous physical barrier separating different neighborhoods. It's just really problematic when the planners make the cross-street green cycle so short that even motorists have trouble getting through (because they're so concerned with not causing traffic backups on the main street). It's bad for bicyclists and even worse for pedestrians, most of whom cross mid-block by looking for a gap in traffic and running for it. A number of pedestrian and bicycle improvements have been promised for 5 or so years now, but the projects have never moved forward (they always cite lack of funding). So in the meantime, some of us just have to deal with these dangerous situations somehow.

The worst road rage incident I ever experienced was at one of these intersections, because I chose to stop at a yellow rather than head into the intersection (since I obviously would not be able to clear the wide intersection before the opposing green, and really neither could a motorist - but I would have been stuck out there longer). A middle-aged woman behind me leaned on her horn and started screaming because I was preventing her from flooring it to get across. I told her that it wasn't safe for me to go, and she just kept cursing at me, and so I cursed her back (probably not a good idea, but her sustained tirade was annoying me). She actually GOT OUT OF HER CAR and tried to start a fight with me. Then she backed down when she realized that I wasn't intimidated by her. The whole thing was just absurd because she was an older woman trying to start a physical fight with a young guy (me).