This is what I did, I was using a custom list view in my section so I don't think you will need the final route.reload I just used it to get my view back in sync after sorting. Note I was sorting from a menu action and so I had access to the node id from dialogOptions.

'use strict';
(function () {
    //create the controller
    function MySettingsSortSubTopicsController($scope, $routeParams, mySettingsResource, $q, navigationService, $route) {
        $scope.editSortView = Umbraco.Sys.ServerVariables.umbracoSettings.appPluginsPath + "/" + $routeParams.section + "/backoffice/Settings/edit-sort.html";
        var dialogOptions = $scope.dialogOptions;
        $scope.save = function (items) {
            if (!$scope.busy) {
                $scope.busy = true;
                var saveIds = [];
                for (var i = 0; i < items.length; i++) {
                    saveIds.push(items[i].id);
                }
                mySettingsResource.saveSortOrder(saveIds, "subtopic").then(function (result) {
                    navigationService.syncTree({ tree: "mySettings", path: ["-1", "topics", $scope.contentId], forceReload: true }).then(function (syncArgs) {
                        $scope.busy = false;
                        $scope.currentNode = syncArgs.node;
                        if ($routeParams.id == $scope.currentNode.id) {
                            $route.reload();
                        }

                    });
                    deferred.resolve(result);
                });
                var deferred = $q.defer();
            }
            return deferred.promise;
        }

        function init() {
            $scope.contentId = dialogOptions.currentNode.id;
            $scope.loaded = true;
        };

        init();

    };
    //register the controller
    angular.module("umbraco").controller('MySettings.SortSubTopicsController', MySettingsSortSubTopicsController);

})();