How to read XML containing character entities using XmlUrlResolver by using Powershell

Question

Using the following Powershell line works correctly until it gets to an XML file containing character entities:

$xml = [xml] (Get-Content $file.Name)

How do you read XML files using Powershell and have it resolve the character entities from the DTD instead of generating errors like this:

Cannot convert value "System.Object[]" to type "System.Xml.XmlDocument". Error: "Reference to undeclared entity 'nbsp'. Line 3, position 324."
Cannot convert value "System.Object[]" to type "System.Xml.XmlDocument". Error: "Reference to undeclared entity 'Oacute'. Line 3, position 239."

Reading XML files is easy when they are valid and don't contain character entities. I have a DTD specified in the XML file with these character entities, but it's not using it. Example start of XML file:

<?xml version="1.0"?>
<!DOCTYPE catalog SYSTEM "manual.dtd">
<catalog ...

How do I turn on the XML resolver in Powershell? The DTD file is in the same folder as the XML files.

I have the code to bypass this issue in C#, but how do I do the following using Powershell?

XML = XMLString;
var dtdPath = HttpContext.Current.ApplicationInstance.Server.MapPath("~/App_Data") + "\\Manual.dtd";
XML = XML.Replace("manual.dtd", dtdPath);
XmlUrlResolver resolver = new XmlUrlResolver();
resolver.Credentials = System.Net.CredentialCache.DefaultCredentials;
XmlReaderSettings settings = new XmlReaderSettings();
settings.DtdProcessing = DtdProcessing.Parse;
settings.ValidationType = ValidationType.None;
settings.XmlResolver = resolver;
XmlReader reader = XmlReader.Create(new System.IO.MemoryStream(System.Text.UTF8Encoding.UTF8.GetBytes(XML)), settings);
var XMLPrimary = XDocument.Load(reader);

Here is my best guess at the Powershell code to do this, but it's still not working. How do you set XmlUrlResolver using Powershell?

$resolver = New-Object -TypeName System.Xml.XmlUrlResolver
$resolver.Credentials = [System.Net.CredentialCache]::DefaultCredentials
$readerSettings = New-Object -TypeName System.Xml.XmlReaderSettings
$readerSettings.DtdProcessing = [System.Xml.DtdProcessing]::Parse
$readerSettings.ValidationType = [System.Xml.ValidationType]::DTD
$readerSettings.XmlResolver = $resolver
$readerSettings.MaxCharactersFromEntities = 2048;
$readerSettings.ValidationFlags = [System.Xml.Schema.XmlSchemaValidationFlags]::ProcessInlineSchema -bor [System.Xml.Schema.XmlSchemaValidationFlags]::ProcessSchemaLocation
$readerSettings.add_ValidationEventHandler(
{
    Write-Host $("`nError found in XML: " + $_.Message + "`n") -ForegroundColor Red
    $script:errorCount++
});
$reader = [System.Xml.XmlReader]::Create($XmlFile.FullName, $readerSettings)
while ($reader.Read()) { }
$reader.Close()