I took IchoTolot's pointer, and thought of it as like four levels in one, and approached each exit individually.
For the replays, I have named them according to which corner they're in; eg. BR = bottom right.
The bottom-right one wasn't much different from my original solution.
The bottom-left one was also fairly simple, though trickier than bottom-right.
Top-left is where things started to get a bit interesting. This one took me a while to work out how exactly to control the crowd and create a turn-around at the top of the stairs, without running out of skills needed to make the path.
And finally, top-right was the hardest one. At first I wondered if this was even possible; the ultimate solution involved some neat delay tactics.
Nice level.