Derek,Tried this sample and it doesn't work right using 3.8.  This is this sample with one extra line: cutVisible: true.
<!DOCTYPE html>
<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
    <!--The viewport meta tag is used to improve the presentation and behavior of the samples 
      on iOS devices-->
    <meta name="viewport" content="initial-scale=1, maximum-scale=1,user-scalable=no">
    <title>Edit rivers and waterbodies</title>
    <link rel="stylesheet" href="http://js.arcgis.com/3.8/js/dojo/dijit/themes/claro/claro.css">
    <link rel="stylesheet" href="http://js.arcgis.com/3.8/js/esri/css/esri.css" />
    <style>
      html,body{height:100%;width:100%;margin:0;overflow:hidden;}
      #map{
        padding:0;
      }
      #header{
        font-size: 1.1em;
        font-family: sans-serif;
        padding-left: 1em;
        padding-top:4px;
        color:#660000;
      }
      .templatePicker {
        border: none;
      }
      .dj_ie .infowindow .window .top .right .user .content { position: relative; }
      .dj_ie .simpleInfoWindow .content {position: relative;}
    </style>
    
    <script src="http://js.arcgis.com/3.8/"></script>
    <script>
      var map;
      
      require([
        "esri/map", 
        "esri/tasks/GeometryService",
        "esri/toolbars/edit",
        "esri/layers/ArcGISTiledMapServiceLayer",
        "esri/layers/FeatureLayer",
        "esri/symbols/SimpleMarkerSymbol",
        "esri/symbols/SimpleLineSymbol",
        "esri/dijit/editing/Editor",
        "esri/dijit/editing/TemplatePicker",
        "esri/config",
        "dojo/i18n!esri/nls/jsapi",
        "dojo/_base/array", "dojo/parser", "dojo/keys",
        "dijit/layout/BorderContainer", "dijit/layout/ContentPane", 
        "dojo/domReady!"
      ], function(
        Map, GeometryService, Edit, 
        ArcGISTiledMapServiceLayer, FeatureLayer,
        SimpleMarkerSymbol, SimpleLineSymbol, 
        Editor, TemplatePicker,
        esriConfig, jsapiBundle,
        arrayUtils, parser, keys
      ) {
        parser.parse();       
        // snapping is enabled for this sample - change the tooltip to reflect this
        jsapiBundle.toolbars.draw.start = jsapiBundle.toolbars.draw.start +  "<br>Press <b>ALT</b> to enable snapping";
       
        // refer to "Using the Proxy Page" for more information:  https://developers.arcgis.com/en/javascript/jshelp/ags_proxy.html
        esriConfig.defaults.io.proxyUrl = "/proxy";    
        //This service is for development and testing purposes only. We recommend that you create your own geometry service for use within your applications. 
        esriConfig.defaults.geometryService = new GeometryService("http://tasks.arcgisonline.com/ArcGIS/rest/services/Geometry/GeometryServer");
        
        map = new Map("map", { 
          basemap: "satellite",
          center: [-96.541, 38.351],
          zoom: 14,
          slider: false 
        });
        map.on("layers-add-result", initEditor);
       
        //add boundaries and place names 
        var labels = new ArcGISTiledMapServiceLayer("http://server.arcgisonline.com/ArcGIS/rest/services/Reference/World_Boundaries_and_Places/MapServer");
        map.addLayer(labels);
        var rivers = new FeatureLayer("http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Hydrography/Watershed173811/FeatureServer/1",{
          mode: FeatureLayer.MODE_ONDEMAND, 
          outFields: ['*']
        });
        var waterbodies = new FeatureLayer("http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Hydrography/Watershed173811/FeatureServer/0",{
          mode: FeatureLayer.MODE_ONDEMAND, 
          outFields: ['*']
        });
        map.addLayers([waterbodies,rivers]);
        function initEditor(evt) {
          var templateLayers = arrayUtils.map(evt.layers, function(result){
            return result.layer;
          });
          var templatePicker = new TemplatePicker({
            featureLayers: templateLayers,
            grouping: true,
            rows: "auto",
            columns: 3
          }, "templateDiv");
          templatePicker.startup();
          var layers = arrayUtils.map(evt.layers, function(result) {
            return { featureLayer: result.layer };
          });
          var settings = {
            map: map,
            templatePicker: templatePicker,
            layerInfos: layers,
            toolbarVisible: true,
            createOptions: {
              polylineDrawTools:[ Editor.CREATE_TOOL_FREEHAND_POLYLINE ],
              polygonDrawTools: [ Editor.CREATE_TOOL_FREEHAND_POLYGON,
                Editor.CREATE_TOOL_CIRCLE,
                Editor.CREATE_TOOL_TRIANGLE,
                Editor.CREATE_TOOL_RECTANGLE
              ]
            },
            toolbarOptions: {
              reshapeVisible: true,
              cutVisible: true
            }
          };
          var params = {settings: settings};    
          var myEditor = new Editor(params,'editorDiv');
          //define snapping options
          var symbol = new SimpleMarkerSymbol(
            SimpleMarkerSymbol.STYLE_CROSS, 
            15, 
            new SimpleLineSymbol(
              SimpleLineSymbol.STYLE_SOLID, 
              new Color([255, 0, 0, 0.5]), 
              5
            ), 
            null
          );
          map.enableSnapping({
            snapPointSymbol: symbol,
            tolerance: 20,
            snapKey: keys.ALT
          });
    
          myEditor.startup();
        }
      });
    </script>
  </head>
  <body class="claro">
    <div id="main" data-dojo-type="dijit/layout/BorderContainer" data-dojo-props="design:'headline'" style="height:width:100%;height:100%;">
      <div data-dojo-type="dijit/layout/ContentPane" id="header" data-dojo-props="region:'top'">
        Edit Hydrography
      </div>
      <div data-dojo-type="dijit/layout/ContentPane" data-dojo-props="region:'left'" style="width: 300px;overflow:hidden;">
        <div id="templateDiv"></div>
        <div id="editorDiv"></div>
      </div>
      <div data-dojo-type="dijit/layout/ContentPane" id="map" data-dojo-props="region:'center'"></div>
    </div>
  </body>
</html>If you can, feel free to move this discussion to another thread and I'll follow it.Thanks again!