In my experience, I found that climbing up on top of the crowd, spreading my arms and legs a bit, and either crab walking or rolling over the top to be quite effective. The people under me didn't like it much, but I got to the edge of the mob and was able to egress to safety. People were packed so tight that even if they wanted to they had no room to pull me back down once I got on top. Of course, there are caveats to such endeavors, but staying in the middle was simply no longer a viable option.

YMMV