CSS fixed element appear over scrollbars

I have seen a few questions about somewhat the same issue, but none of the specified answers actually work for this one.

Consider the following snippet :

$(function () {
  $(window).on('scroll', function () {
    /**
      THIS SHOULD NOT BE CALLED!!!
      So, change some colors to warn about it, if it happens.
    */
    $('#content').css('background-color', 'red');
  });
});

body {
  margin:0;
  padding:0;
    
  height: 100%;
  width: 100%;
}

#container {
  position: absolute;
    
  height: 100%;
  width: 100%;
  z-index: 9999999;
    
  overflow: auto;
}

#nav {
  background-color:rgb(50,50,50);
  color: white;

  position: fixed;
  left: 0;
  top: 0;
  
  width: 100%;
  height: 30px;
  padding-top: 10px;
  z-index: 100;
}

#content-wrapper {
  background-color:rgb(200,200,200);

  min-height: 100%;
  height: auto !important;
  width: 100%;
  z-index:2;
}

#content {
  padding-top: 40px;
  padding-bottom: 40px;
}

#footer {
  background-color: rgb(220, 220, 240);
  
  position: fixed; 
  left: 0;
  bottom: 0;

  height: 30px;
  width: 100%;
  padding-top: 10px;
  z-index: 9999;
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

<div id="container">
  <div id="nav">
    Navbar
  </div>
    
  <div id="content-wrapper">
    <div id="content">
      <div>
        Begin
      </div>
      <div style="height: 600px;">
        ...
      </div>
      <div>
        End
      </div>
    </div>
  </div>
    
  <div id="footer">
    Footer
  </div>
</div>

The scrollbar goes underneath nav and footer. Since this is very important that only the container element scrolls (the BODY element must not scroll), how can I fix this? Is it possible?

The HTML structure should essentially be as suggested in this question (fixed nav, full height content, etc.). I have tried several tricks; modifying z-indexes, wrapping things around, etc., I'm at a lost here.

The targeted browser is Google Chrome, as this is the adopted browser in use for this application. The ideal solution would make the fixed element adjust their width to compensate for the overflow: auto; on the container element.

Demo in this fiddle

An alternative approach here would be to only scroll the #content-wrapper from your example. Here's a basic example of how this might be done:

HTML

<div id="container">
    <div id="nav">
        Navbar
    </div>

    <div id="content-wrapper">
        <div id="content">
            <div>
                Begin
            </div>
            <div style="height: 600px;">
                ...
            </div>
            <div>
                End
            </div>
        </div>
    </div>

    <div id="footer">
        Footer
    </div>
</div>

CSS

body {
    margin:0;
    padding:0;
    height: 100%;
    width: 100%;
}

#container {
    position: absolute;
    height: 100%;
    width: 100%;
    overflow: hidden;
}

#nav {
    background-color:rgb(50,50,50);
    color: white;
    position: fixed;
    left: 0;
    top: 0;
    width: 100%;
    height: 30px;
    padding-top: 10px;
}

#content-wrapper {
    position:absolute;
    top:40px;
    bottom:40px;
    left:0;
    right:0;
    background-color:rgb(200,200,200);
    width: 100%;
    overflow:scroll;

}

#footer {
    background-color: rgb(220, 220, 240);
    position: fixed; 
    left: 0;
    bottom: 0;
    height: 30px;
    width: 100%;
    padding-top: 10px;
}