jQuery Sortable JSON Update Issue

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/css/bootstrap.min.css">
<ol id="my-nav">
  <li data-id="unique-id-here" data-label="My Label">
    <span>My Label</span>
    <input type="text" class="label-change form-control" placeholder="Type here to see the impact">
    <ol>
      <li data-id="unique-id-here" data-label="My Sub Label">
        <span>My Sub Label</span>
        <input type="text" class="label-change form-control" placeholder="Type here to see the impact">
        <ol>
          <!-- PLACEHOLDER FOR SUBMENU -->
        </ol>
      </li>
    </ol>
  </li>
</ol>

<h4>OUTPUT HERE</h4>
<textarea id="output" class="form-control" placeholder="">[[{"label":"My Label","id":"unique-id-here","children":[[{"label":"My Sub Label","id":"unique-id-here","children":[[]]}]]}]]</textarea>

SCSS

body.dragging,
body.dragging * {
  cursor: move !important;
}

// GRAB ATTENTION.
input[type="text"] {
  border-color: red;
}

#my-nav {
  padding-left: 0;
  list-style-type: none;
  overflow: hidden;

  ol {
    padding-left: 0;
    margin-left: 20px;
    list-style-type: none;
  }

  li {
    padding: 5px 10px;
    background-color: #f8f8f8;
    color: #333;
    border: 1px solid #999;
    border-radius: 3px;
    margin-bottom: 10px;
    box-shadow: 0 0 5px rgba(0, 0, 0, 0.2);
    cursor: move;

    &.placeholder {
      position: relative;
      border-style: dashed;
      background-color: #ededed;
      min-height: 34px;

      &:before {
        position: absolute;
      }
    }

    &.dragged {
      position: absolute;
      top: 0;
      opacity: .5;
      z-index: 2000;
      box-shadow: 0 0 15px rgba(0, 0, 0, 0.5);

      i.icon-move {
        color: var(--primary);
      }
    }

    &.highlight {
      background: gray;
      color: lightgray
    }

    &:first-of-type {
      margin-top: 10px;
    }
  }

  i.icon-move {
    cursor: pointer;
    color: #999;
    padding: 5px;
  }
}

.dd {
  position: relative;
  display: block;
  margin: 0;
  padding: 0;
  max-width: 600px;
  list-style: none;
  font-size: 13px;
  line-height: 20px;
}

.dd-list {
  display: block;
  position: relative;
  margin: 0;
  padding: 0;
  list-style: none;
}

.dd-list .dd-list {
  padding-left: 30px;
}

.dd-item,
.dd-empty,
.dd-placeholder {
  display: block;
  position: relative;
  margin: 0;
  padding: 0;
  min-height: 20px;
  font-size: 13px;
  line-height: 20px;
}

.dd-handle {
  display: block;
  height: 30px;
  margin: 5px 0;
  padding: 5px 10px;
  color: #333;
  text-decoration: none;
  font-weight: bold;
  border: 1px solid #ccc;
  background: #fafafa;
  border-radius: 3px;
  box-sizing: border-box;
}

.dd-handle:hover {
  color: #2ea8e5;
  background: #fff;
}

.dd-item>button {
  position: relative;
  cursor: pointer;
  float: left;
  width: 25px;
  height: 20px;
 ...

JavaScript

/** OUR CODE STARTS AT LINE#702 */

/* ===================================================
 *  jquery-sortable.js v0.9.13
 *  http://johnny.github.com/jquery-sortable/
 * ===================================================
 *  Copyright (c) 2012 Jonas von Andrian
 *  All rights reserved.
 *
 *  Redistribution and use in source and binary forms, with or without
 *  modification, are permitted provided that the following conditions are met:
 *  * Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *  * Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *  * The name of the author may not be used to endorse or promote products
 *    derived from this software without specific prior written permission.
 *
 *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 *  ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 *  WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 *  DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY
 *  DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 *  (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 *  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 *  ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 *  (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 *  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 * ========================================================== */

! function($, window, pluginName, undefined) {
  var eventNames,
    containerDefaults = {
      // If true, items can be dragged from this container
      drag: true,
      // If true, items can...