One weird way to move fast through a crowd that I've found is to keep your hands up. Not sure why, but when I'm doing this, most of the people seem to get out of the way. Works almost every time.
A strategy that I've seen suggested that works very well for me is to just look at your feet. You don't need to care about where people bodies are, bodies follow feet, watch your steps, not only you won't step on or get stepped on, but you are also less likely to hit other people.
I also won't see your hands up.
I think part of the reason hands up work is also simply because you take less space with your hands up (you body becomes narrower overall).
