Found the answer elsewhere.
You can access the symbol by doing:
var myComp = AdobeEdge.getComposition("compositionname");
var mySymbol = myComp.getSymbol("symbolname");
// var myStage = myComp.getStage(); if all you want is the stage
Then you can do things like:
$(".play").mouseenter(function(e) {
mySymbol.play();
});