Testing using the Google Structured Data Test Tool (https://search.google.com/structured-data/testing-tool) showed that the Article objects were registering as separate objects and not part of the WebPage object. After many tests, I found that using a combination of the itemList and itemListElement was the only way to get Google to identify the list of Articles as sub objects.
Here is an example of the HTML that I was able to get to pass the test.
<!DOCTYPE html>
<html lang="en-US" itemscope itemtype="https://schema.org/WebPage">
<head>
<title>Schema Testing</title>
<meta itemprop="copyrightYear" content="2018" />
<!-- LOCAL META VARIABLES -->
<title itemprop="name" property="og:site_name">Add no wrap by Bryan Myers - Senior Front-end Web Designer</title>
<meta itemprop="about description" content="Add no wrap by Bryan Myers - Senior Front-end Web Designer" />
<meta itemprop="keywords" content="Add no wrap, Web Article, Bryan Myers, The Web Guy" />
<meta itemprop="dateCreated datePublished" content="" />
<meta itemprop="dateModified lastReviewed" content="2018-07-01" />
</head>
<body itemprop="mainEntity" itemscope itemtype="https://schema.org/ItemList">
<div itemprop="itemListElement" itemscope itemtype="https://schema.org/Article">
<div itemprop="author">Bryan Myers</div>
<div itemprop="publisher" itemscope itemtype="https://schema.org/Organization">
<div itemprop="name url">www.bryan-myers.com</div>
<div itemprop="logo" itemscope itemtype="https://schema.org/ImageObject"><img itemprop="url" src="https://www.bryan-myers.com/favicon.png"></div>
</div>
<div itemprop="url">www.bryan-myers.com/schema.html</div>
<div itemprop="datePublished">2018-7-26</div>
<div itemprop="dateModified">2018-7-26</div>
<div itemprop="headline">2018-7-26</div>
<div itemprop="position">1</div>
<div><img itemprop="image" src="https://www.bryan-myers.com/favicon.png"></div>
<div itemprop="mainEntityOfPage">
This is the stuff!
</div>
</div>
<div itemprop="itemListElement" itemscope itemtype="https://schema.org/Article">
<div itemprop="author">Bryan Myers</div>
<div itemprop="publisher" itemscope itemtype="https://schema.org/Organization">
<div itemprop="name url">www.bryan-myers.com</div>
<div itemprop="logo" itemscope itemtype="https://schema.org/ImageObject"><img itemprop="url" src="https://www.bryan-myers.com/favicon.png"></div>
</div>
<div itemprop="url">www.bryan-myers.com/</div>
<div itemprop="datePublished">2018-7-26</div>
<div itemprop="dateModified">2018-7-26</div>
<div itemprop="headline">2018-7-26</div>
<div itemprop="position">2</div>
<div><img itemprop="image" src="https://www.bryan-myers.com/favicon.png"></div>
<div itemprop="mainEntityOfPage">
Content goes here!
</div>
</div>
</body>
</html>
I am still not quite sure if the mainEntityOfPage object is correct on the site. According to https://schema.org/mainEntityOfPage the object can be either a CreativeWork or a URL. It seems odd to me that an Article, a CreativeWork object in and of itself, would need CreativeWork to define one of the primary properties. And if the Article were a URL, that really wouldn't be the an Article, would it?