I really wouldn't suggest doing this, for reasons that others already stated, but you can always get a handle to the angular $scope of a given element in some jquery handler. Just define your controller as anybody normally would (in the body of a script).
success: function(data){
... //splits and whatnot
var $scope = angular.element($("div[ng-controller='SplitController']")).scope()
$scope.$apply(function(){
$scope.splits = splits;
})
}
You can't define a controller like you're doing because ng-app is going to run on document.ready. It will be looking for the controller you specified with ng-controller which has yet to be defined. It's perfectly okay for you to define a SplitController that doesn't initialize 'splits' or any data, because ng-repeat will be watching for changes to 'splits' and will keep the DOM up to date.